Victor Kaftal

Ph.D: Tel Aviv University Israel, 1979 (Mathematics)

Laurea: Universita' degli Studi di Milano Italy, 1970 (Physics)

My main research areas are Operator Theory and Operator Algebras. In recent years,  I have been working mainly on:
• frame theory in B(H) and in C*-modules,
• decomposition of positive operators into positive combinations of projections or into sums of projections, in the setting of B(H), of von Neumann algebras, and of  C*-algebras.
• sums of commutators and linear combination of projections in finite C*-algebras
• strict comparison of projections and of positive elements in C*-algebras

1979 -1981 Visiting Assistant Professor, University of Cincinnati,

1981 -1985 Assistant Professor, University of Cincinnati,

09-1984 -12-1984 Member, Mathematical Sciences Research Institute, Berkeley, CA

1985 -1991 Associate Professor, University of Cincinnati,

09-1988 -03-1989 Visiting Scholar, University of Pennsylvania, Philadelphia, PA & , Texas A&M University, College Station, TX

1991 -To Present Professor,

09-1998 -03-1999 Visiting Scholar, Texas A&M Univ, College Station, TX; U. Waterloo, Ontario;, U. Nebraska, Lincoln, NE

09-2007 -03-2008 Visiting Scholar, Texas A&M Univ, College Station, TX;, Univ. Roma, Tor Vergata, Roma, Italy

09-2014 -10-2014 Visiting Scholar, University Lousiana, Lafayette, LA

10-2014 -11-2014 Visting Scholar, Texas A&M University, College Station, TX

Grant: #DMS-1343888 Investigators:Kaftal, Victor 08-15-2013 -07-31-2014 National Science Foundation The Eleventh East Coast Operator Algebras Symposium Role:PI $31,760.00 Active Level:Federal

Grant: #245660 Investigators:Victor Kaftal 09-01-2012 -08-31-2017 Simons Foundation Collaboration Grants for Mathematicians Role:PI 35,000 Active Type:Grant Level:National

Grant: #DMS-0649960 Investigators:Halpern, Herbert; Kaftal, Victor; Peligrad, Costel; Weiss, Gary; Zhang, Shuang 04-01-2007 -03-31-2009 National Science Foundation Collaborative Research: Operator Theory/Operator Algebras, GPOTS 07-08 Role:PI $25,000.00 Closed Level:Federal

Grant: #Award Number: 245660 Investigators:Kaftal, Victor 09-01-2012 -08-31-2017 Simons Foundation Finite Sums of Projections Role:PI $7,000.00 Active Level:Private Non-Profit

Peer Reviewed Publications

Kaftal, V P. W. Ng, S. Zhang, Commutators and linear spans of projections in certain finite C*-algebras, Journal Functional Analysis (2014), 266, No 4, 1883-1912.

Halpern, H., Kaftal, V., Ng. P.W., Zhang, S. Finite sums of projections in von Neumann algebras, Trans. Amer Math Soc (2013) 365, 2409-2445

Kaftal. V., Ng. P.W., Zhang, S. Finite sums of projections in purely infinite simple C*-algebras with torsion K_0, Proc. Amer Math Soc, (2012), 140, No 9, 3219-3227.

Kaftal, V., Ng, P.W., Zhang, S.  Projection decompositions in multiplier algebras. Mathematische Annalen,  (2012) 352, No 3, 543-566.

Kaftal. V., Ng. P.W., Zhang, S. Positive combinations and sums of projections in purely infinite simple C*-algebras and their multiplier algebras, Proc. Amer Math Soc (2011) 139, 2735-2746.

Kaftal, V. & Weiss G.  B(H) Lattices, density, and arithmetic means ideals. Houston J. Math. (2011) 37, 233-283.

Kaftal, V. & Weiss G.  Majorization and arithmetic mean ideals. Indiana Univ. Math J., (2011) 60, 1393-1424.

Kaftal, V. &Weiss, G.  An infinite dimensional Schur-Horn theorem and majorization theory. J. Funct. Anal. (2010) 259, 3115-3162.

Kaftal, V., & Weiss, G.  Traces on operator ideals and arithmetic means. Journal of Operator Theory, (2010) 63, No 1, 3-46

Kaftal. V., Ng. P.W., Zhang, S. Strong sums of projections in von Neumann factors. J. Funct. Anal. (2009) 257, 3115-3162

Kaftal, V., Larson, D., & Zhang, S. Operator valued frames. Transactions AMS  (2009) 361 (12) 6349-6385.

Kaftal, V. & Pal, D.  Does third degree price discrimination reduce social welfare? Southern Economic J. (2008) 75 (2) 558-573.

Kaftal, V., Larson, D. & Zhang, S. Operator valued frames on C*-modules. Contemporary Math., (2008) 451, 363-408

Kaftal, V., & Weiss, G. Second order arithmetic means in operator ideals. Operators and Matrices (2007) 1,  235-256.

Kaftal, V., & Weiss, G.  Soft ideals and arithmetic means. Integral Eq Operator Theory J., (2007) 58, 363-405.

Bryc, W., & Kaftal, V. Strong mixing coefficients for non-commutative Gaussian processes. Proc. Amer. Math. Soc, (2003) 132 (2), 523-534.

Kaftal, V., & Weiss, G. Traces ideals, and arithmetic means. Proceedings National Academy of Sciences, (2002) 99 (11), 7356-7360.

Bakonyi, M., Kaftal, V., Weiss, G., & Woerdeman, H. Bounds for operator/Hilbert Schmidt norm minimization using entropy. Indiana University Math. J,  (1997) 46 (2)  405-426.

Bakonyi, M., Kaftal, V., Weiss, G., & Woerdeman, H. Norm bounds for operator extensions. Journal of Mathematical Analysis and Applications, (1995) 194, 352-367.

Bakonyi, M, Kaftal, V., Weiss, G., & Woerdeman, H.  Maximum entropy and joint norm bounds for operator extensions. Operator Theory: Advances and Appl, (1993) 64, 23–32.

Kaftal, V., Larson, D., & Weiss, G.  Quasitriangular subalgebras of semifinite von Neumann algebras are closed. J. Funct. Anal, (1992) 107 (2), 387-401.

Kaftal, V.  Type decompositions for von Neumann algebras embeddings. J. Func. Anal, (1991) 98(1), 169-193.

Halpern, H., Kaftal, V., & Zsidó, L. Finite weight projections in von Neumann algebras. Pacific J. Math, (1991) 147(1), 81-121.

Berman, K., Halpern, H., Kaftal, V., & Weiss, G.  Matrix norm inequalities and the relative Dixmier property. Int. Eq. and Oper. Th. J., (1988) 11, 28-48.

Halpern, H., Kaftal, V., & Weiss, G.  Matrix pavings in B(H). Oper. Th.: Advances and Applications, (1987) 24, 201-214.

Halpern, H., & Kaftal, V. Compact operators in type IIIlambda and type IIIo factors, II. Tohôku Math. J., (1987) 39, 153-173.

Halpern, H., & Kaftal, V.  Compact operators in type IIIlambda and type IIIo factors. Math. Ann., (1986) 273, 251-270.

Kaftal, V., & Mercer, R. Spectral projections of L1-operators in type IIIlambda von Neumann algebras. Integr. Eq. and Oper. Th., (1986) 9, 679-693.

Kaftal, V., & Weiss, G. A Riemann type theorem for unconditional convergence of operators. Proc. AMS., (1986) 98, 431-436.

Halpern, H., Kaftal, V., & Weiss, G. Matrix pavings and Laurent operators. J. Oper. Th., (1986) 16, 355-374.

Halpern, H., Kaftal, V., & Weiss, G. The relative Dixmier property in discrete crossed products. J. Funct. Anal., (1986) 69, 121-140.

Kaftal, V., & Weiss, G. Compact derivations relative to semifinite von Neumann algebras. J. Funct. Anal., (1986) 62, 202-220.

Cho, S.J., & Kaftal, V. A generalization of the Weyl-von Neumann theorem to semifinite von Neumann algebras. Indiana Univ. Math. J., (1982) 31, 57-63.

Kaftal, V. Almost Fredholm operators in von Neumann algebras. Integr. Eq. and Oper. Th., (1982) 5, 50-70.

Kaftal, V. Relative weak convergence of vectors in semifinite von Neumann algebras. Proc. AMS., (1982) 84, 89-94.

Kaftal, V. On the theory of compact operators in von Neumann algebras II. Pacific J. Math., (1978) 79, 129-137.

Kaftal, V. On the theory of compact operators in von Neumann algebras I. Indiana Univ. Math. J., (1977) 26, 447-457.

Kaftal, V P. W. Ng, S. Zhang, Strict comparison of projections and positive combinations of projections in certain multiplier algebras. J. Oper. Theory. (2015), 73, No1, 187-210

Dragan, C., Kaftal, V., Sums of equivalent sequences of positive operators in von Neumann factors. Houston Journal of Mathematics, (2016), 42, No. 3, 991-1017.

Kaftal V, Ng, P.W., Zhang, S., Strict comparison of positive elements in multiplier algebras, Canadian Journal of Mathematics, (2017) 69, 373-407.

Bemrose, T., Casazza, P. G.,  Kaftal, V. , and Lynch P.G., The unconditional constant for Hilbert space frame expansions, Linear Algebra and its Applications. (2017) 521, 1-18

V. Kaftal, J. Loreaux, Kadison’s Pythagorean theorem and essential codimension, Integr. Equ. Oper. Theory (2017) 87, 565–580

Kaftal V, Ng, P.W., Zhang, S,  The minimal ideal in a multiplier algebra, Journal of Operator Theory, (2018) 79, No. 2,  419-462.

Kaftal V., and Larson D., Admissible sequences of positive operators, Trans. Amer. Math. Soc. 371 (2019), 3721-3742

Peer Reviewed Conference/Workshop Proceedings

Kaftal. V., Ng. P.W., Zhang, S. Positive combinations of projections in von Neumann algebras and purely infinite simple C*-algebras, Science China Mathematics, (2011) 54, 1-10 .

Kaftal, V. & Weiss, G. A survey on the interplay between arithmetic ideals, traces, lattices of operator ideals, and an infinite Schur-Horn majorization theorem. Hot topics in Operator Theory, Theta P. (2008) 101-135.

Berman, K., Halpern, H., Kaftal, V., & Weiss, G. Some C4 and C6 norm inequalities related to the paving problem. Proceedings of Symposia in Pure Mathematics, (1990) 51(2), 29-41.

Halpern, H., Kaftal, V., & Zsidó, L.  Finite weight projections in von Neumann factors. Proceedings of Symposia in Pure Mathematics, (1990) 51(2), 143-152.

Kaftal V, Ng, P.W., Zhang, S., Projections in C*-algebras and strict comparison, Hot topics in operator theory, Theta 2016, 53-74.

Invited Presentations

Kaftal V (07-2014. ) Linear combinations of projections in C*-algebras and their multiplier algebras .25th International Conference on Operator Theory, Timisoara, Romania. Conference. . Level:International

Kaftal V (05-2014. ) Linear combinations of projections in C*-algebras .Great Plains Operator Theory Symposium, Kansas State University. Conference. . Level:International

Kaftal, V (04-2014. ) Positive linear combinations of projections .AMS Special Sessionon Progress in Noncommutative Analysis, Albuquerque, NM. Conference. . Level:National

(02-2013. ) Positive linear combinations of projections in certain finite C*-algebras and in their multiplier algebras .Wabash Seminar, Crawfordsville, IN. Level:Regional

(10-2012. ) Linear combinations of projections in finite C*-algebras .10th ECOAS, Knoxville, TN. Conference. . Level:National

(07-2012. ) Linear combinations of projections .24rth International Conference on Operator Theory,, Timisoara, Romania. Conference. . Level:International

(05-2012. ) Positive combinations of projections .Great Plains Operator Theory Symposium (GPOTS), Houston, TX. Conference. . Level:International

(05-2011. ) Finite sums of projections in operator algebras .Canadian Operator Symposium 2011, U. Victoria, Victoria, BC. Conference. . Level:International

(01-2011. ) Finite Sums of Projections .Special Session AMS Annual Meeting, New Orleans. Conference. . Level:National

(01-2011. ) Equal-norm perturbations of finite frames .Workshop in Analysis and Geometry, LSU, Baton Rouge, LA. Workshop. . Level:National

(07-2010. ) 23rd Conference in Operator Theory, Timisoara, Romania. Level:International

(01-2010. ) AMS Special Session, San Francisco, CA. Level:National

(01-2010. ) Workshop on Optimal Frames , San Francisco, CA. Level:National

(07-2009. ) GPOTS, Boulder, Co.

(03-2009. ) AMS Special Session, Urbana, IL. Level:Regional

(07-2008. ) 22nd Conference in Operator Theory, Timisoara, Romania. Level:International

(04-2008. ) AMS Special Session, Bloomington, IN. Level:Regional

(04-2008. ) Nebraska-Iowa Functional Analysis Seminar, Iowa City, IA. Level:Regional

(05-2007. ) GPOTS, Lincoln, NE. Level:International

(08-2006. ) Concentration Week in Analysis, College Station, TX. Level:National

(01-2006. ) AMS Special Session, S. Antonio, TX. Level:National

(07-2003. ) ICAA, S. Africa. Level:International

(01-2003. ) AMS Special Session, Baltimore, MD. Level:National

(07-2002. ) Nonselfadjoint Operator Algebras Workshop, Toronto, ON Canada. Level:International

(07-2001. ) 18th Conference in Operator Theory, Timisoara, Romania. Level:International

(06-2001. ) GPOTS, NH. Level:International

(04-1999. ) Nebraska-Iowa Functional Analysis Seminar, Iowa City, IA. Level:Regional

(07-1996. ) IWOTA, Bloomington, IN. Level:International

(10-1993. ) AMS Special Session, College Station, TX. Level:Regional

(04-1993. ) Operator Theory and Wavelet Conference, Raleigh, NC. Level:National

(01-1993. ) AMS Special Session, S. Antonio, TX. Level:National

(11-1992. ) Operator Theory Conference, College Station, TX. Level:National

(10-1992. ) AMS Special Session, Dayton, OH. Level:Regional

(09-1991. ) Wabash Seminar, Crawforsdville, IN. Level:Regional

(05-1991. ) GPOTS, College Station, TX. Level:International

(04-1991. ) Wabash Conference, Indianapolis, IN. Level:National

(01-1991. ) AMS Special Session, San Francisco, CA. Level:National

(05-1990. ) GPOTS, Albuquerque, NM. Level:International

(07-1988. ) 36th AMS Summer Research Institute .Durham, NH, Level:National

(05-1988. ) GPOTS, Indianapolis, IN. Level:International

(10-1987. ) AMS Special Session, Lincoln, NE. Level:Regional

(08-1986. ) International Congress of Mathematicians, Berkeley, CA. Level:International

(07-1985. ) 10th International Conference in Operator Theory, Bucharest, Romania. Level:International

(05-1985. ) GPOTS, College Station, TX. Level:International

(05-1984. ) GPOTS, Ames, IA. Level:International

Kaftal V. (05-2015. ) Ideals in multiplier algebras of simple finite C*-algebras .Great Plain Operator Theory Symposium, West Lafayette. Conference. . Level:International

(06-1983. ) GPOTS, Boulder, CO. Level:International

Kaftal, V (07-2016. ) The integer in Kadison's Pythagorean Theorem and essential codimension .26th Conference in Operator Theory, Timisoara, Romania. Conference. . Level:International

(08-1980. ) Summer Research Institute on Operator Algebras, Kingston, ON Canada. Level:International

Kaftal, V (05-2016. ) The integer in Kadison's Pythagorean Theorem and essential codimension. Great Plains Operator theory Seminar, Urbana, IL. Level:International

(12-1979. ) Wabash Seminar, Crawforsdville, IN. Level:Regional

Kaftal, V (04-2017. ) The Minimal Ideal in Multiplier Algebras .Operators on Hilbert Spaces Symposium, Columbus OH. Level:Regional

(05-1979. ) Israel Math Soc, Beer Sheva, Israel. Level:National

Kaftal, V (10-2017. ) Ideals in Multiplier Algebras .• 15thth East Coast Operator Algebras Symposium, Lafayette, LA. Level:National

(01-1979. ) AMS , Biloxi, MS. Level:National

Kaftal, V (07-2018. ) Purely Infinite Corona Algebras. 27th Conference on Operator Theory, Timisoara, Romania. Level:International

Kaftal, V (07-2018. ) Diagonals of positive operators, an alternative approach. 6th Summer Workshop of Operator Theory (SWOT), Krakow, Poland. Level:International

Kaftal, V (06-2018. ) Purely Infinite Corona Algebras .Great Plains Operator Theory Symposium, Oxford, OH. Level:International

Lecture

(01-2008. ) Rome, Italy.

Kaftal V (11-2014. ) Linear combinations of projections in operator algebras .Charlottestville. Other Institution. Level:University

(11-2007. ) Lafayette, LA.

Kaftal V (11-2014. ) Compact operators in type III factors .Charlottestville, VA. Other Institution. Level:Department

(11-2007. ) College Station, TX.

Kaftal V (10-2014. ) Frame theory methods in Kadison's Pythagorean theorem and in sums of projections problems .Houston, TX. Other Institution. Level:University

(12-2001. ) Rome, Italy.

Kaftal, V (10-2014. ) The role of the frame transform and its Fredholm index in various operator theory problems. College Station, TX. Other Institution. Level:University

(04-1999. ) Waterloo, ON Canada.

Kaftal V (09-2014. ) Intriguing integers in some operator theory problems .Lafayette, LA. Other Institution. Level:University

(04-1999. ) Lincoln, NE.

(02-1999. ) College Station, TX.

(1990. ) Dayton, OH.

(02-1989. ) Houston, TX.

(03-2013. ) Linear combinations of projections in C* and W* algebras .College Station, TX. Other Institution. Level:Regional

(01-1989. ) College Station, TX.

(11-1988. ) Philadelphia, PA.

(12-1986. ) Milan, Italy.

(1986. ) Milan, Italy.

(09-1985. ) Stuttgart, West Germany.

(09-1985. ) Copenhagen, Denmark.

(11-1984. ) Berkeley, CA.

(11-1984. ) Los Angeles. CA.

(12-1983. ) Linz, Austria.

(12-1983. ) Milan, Italy.

(1983. ) Milan, Italy.

(12-1981. ) Italy.

(12-1981. ) Milan, Italy.

(02-1981. ) College Station, TX.

(05-1980. ) Athens, GA.

(03-1980. ) New York, NY.

(02-1979. ) Halifax, NS Canada.

(02-1979. ) West Lafayette, IN.

(02-1979. ) Toronto, ON Canada.

(1979. ) Toronto, ON Canada.

Kaftal V. (01-2015. ) The role of finiteness of the tracial simplex for certain C*-algebras and their multiplier algebras .University Waterloo. Other Institution. Level:Regional

(Coordinator of the Calculus Sequence for 2011-2013 ) Type:Departmental Service Level:Department 09-2011

(A&S Senate ) Member Type:University/College Service Level:College 09-2011

(Coordinator of Calculus ) Committee Chair Type:Departmental Service Level:Department 09-2011

(A&S Senate ) Member Type:University/College Service Level:College 09-2011

(Academic Program Review Committee ) Committee Chair Type:University/College Service Level:College 09-2011 -06-2012

(Calculus Committee ) Committee Chair Type:Departmental Service Level:Department 07-2011

(Graduate Advisors Committee ) Committee Chair Type:Departmental Service Level:Department 09-2010 -08-2011

(Graduate Affairs Committee ) Committee Chair Type:Departmental Service Level:Department 09-2010 -08-2011

Real Analysis Level:Graduate

15-MATH-252 CALCULUS II Level:Undergraduate

15-STAT-241 INTRO TO STATISTICS Level:Undergraduate

Real Analysis Level:Graduate

15-MATH-251 CALCULUS I Level:Undergraduate

15-MATH-251 CALCULUS I Level:Undergraduate

15-MATH-252 CALCULUS II Level:Undergraduate

15-MATH-253 CALCULUS III Level:Undergraduate

Calculus 1 Level:Undergraduate