Costel Peligrad

Costel Peligrad

Professor

French Hall

4508

A&S Mathematical Sciences - 0025

Professional Summary

ACADEMIC APPOINTMENTS
Researcher, Department of Mathematics, INCREST, Bucharest, Romania, 1977-1982
Visiting Professor, University of Rome, Italy, 1982-1983
Visiting Professor, Worcester Polytechnic Institute, Worcester, Massachussetts, 1983-1984
Associate Professor, University of Cincinnati, 1984-1989
Professor, University of Cincinnati, 1989-

Education

PhD in Mathematics, University of Bucharest Bucharest, Romania, 1980 (Nonselfadjoint Operator Algebras)

Research and Practice Interests

Operator Algebras and Abstract Harmonic Analysis.
My research is concerned with C*- and von Neumann Algebras and their automorphism groups and with nonsefadjoint operator Algebras, including invariant subspaces.

Research Support

04-01-2013 -06-01-2013 Taft Travel for Research Grant

Grant: #0649960 Investigators:H. Halpern, V. Kaftal, C. Peligrad, S. Zhang, G. Weiss 04-15-2007 -10-15-2008 NSF Collaborative Research, Operator Theory/Operator Algebras, GPOTS07-08 Role:Co-PI $25,000 Completed Type:Grant Level:International

2003 Taft Travel Grant Type:Grant

1998 Taft Travel Grant Type:Grant

1995 Taft Research Travel Grant Type:Grant

1993 Taft Research Travel Grant Type:Grant

1990 Taft Travel Grant Type:Grant

1989 Taft Research Grant Type:Grant

1987 Taft Travel Grant Type:Grant

1985 -1987 NSF Grant Type:Grant

1981 Romanian Academy Prize Type:Grant

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:Collaborator $25,000.00 Closed Level:Federal

Abbreviated Publications

Peer Reviewed Publications

Peligrad, C., Compact Group Actions on Operator Algebras and their Spectra,  Mathematica Scandinavica Vol 126, No. 2 (2020), 276-292.

Peligrad, C., Invariant subspaces of generalized Hardy algebras associated with compact abelian group actions on W*-algebras, Houston J. Math. Vol. 46, Nr. 2 (2020), 1-25.

Peligrad, C. Duality for compact group actions on operator algebras and applications: irreducible inclusions and Galois correspondence,  Internat. J. Math., Vol. 31, Nr.9 (2020), 12 pages.

 Peligrad, C. A solution of the maximality problem for one-parameter dynamical systems, Adv. Math. 329 (2018), 742-780.

Peligrad, C, Invariant subspaces of algebras of analytic elements associated with periodic flows on W*-algebras, Houston Journal of Mathematics, 42 (4) 2016, 1331-1344..

The limiting spectral distribution in terms of spectral density (with M. Peligrad), Random Matrices: Theory and Applications, 5 (2016), 19 pp.

On the functional CLT for stationary Markov Chains started at a point (with D. Barrera and M. Peligrad), Stochastic Processes and their Applications, 126 (2016), 1885-1900.

F. Merlevede., C.Peligrad and M. Peligrad, The universality of spectral limit for random matrices with martingale differences entries , Random Matrices:Theory and Applications, Vol.4, 1 (2015). [Link]

 Merlevede, F., Peligrad, C. and Peligrad, M., Reflexive operator algebras on Banach spaces, Pacific Journal of Mathematics 267-2 (2014), 451--464

  Dumitru, R.and  Peligrad, C., Nuclear and type I C*-crossed products, J. Operator Theory, 69:1(2013), 287-296. 

Peligrad, C. and Zsido, L., Maximal subalgebras associated with periodic flows, Journal of Functional Analysis, 262 (2012), 3626-3637.  

 Longla, M., Peligrad, C. and Peligrad, M.: On the functional CLT for reversible Markov chains with nonlinear growth of the variance, Journal of Applied Probability, 49 (4), (2012), 1091-1105. 

 Dumitru, R. and Peligrad, C., Spectra for compact quantum group actions on C*-algebras , Transactions of the Amer. Math. Soc. 364 (2012), 3699-3713.  

Merlevede, F., Peligrad, C. and Peligrad, M., Almost Sure Invariance Principles via Martingale Approximation , Stochastic Proc. and their Appl. 122 (2012), 170-190
 
 
 
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Peligrad, C. and Peligrad, M., On the invariance principle under martingale approximation, Stochastics and Dynamics, 11 (2011), No.1, 95-105.

 

Dumitru, R., Peligrad, C. and Visinescu, B., Reflexivity of operator algebras of finite strict multiplicity, Operators and Matrices, 5 (2011), 221-226.  

Peligrad, C., A Galois correspondence for compact group actions on C*-algebras, Journal of Functional Analysis, 261 (2011), 1227-123
 

Dumitru, R. and Peligrad, C., Compact quantum group actions on C*-algebras and invariant derivations, Proc. Amer. Math. Soc. 135 (2007), 3977-398.  
 

Dumitru, R., Peligrad, C. and Visinescu, B., Automorphisms inner in the local multiplier algebra and Connes spectrum,in: Operator theory 20, Theta Ser. Adv. Math.6, Theta, Bucharest (2006), 75–80. 
.

 Peligrad, C., Strictly cyclic operator algebras on Banach spaces, Integral Equations and Operator Theory, 48 (2004), 557-560. 
 

 Peligrad, C. and Zsido, L., Open projections of C*-algebras: Comparison and regularity, Proceedings of the 17th OT Conference, Timisoara, Romania, Theta (2000), 285 - 300. 

  Szymanski, W. and Peligrad, C., Saturated actions of Hopf algebras on C*-algebras, Math Scandinavica,  75 (1994), 217-239.  
 

 Peligrad, C., (1988). Locally compact group actions on C*-algebras and   compact subgroups. J. Func. Analysis 76, 126-140. 
 
 Goodman, F., Jorgensen P., & Peligrad, C.,(1986). Smooth derivations commuting with Lie group actions. Math. Proc. Cambridge Phil. Soc. 99, 307-314.
 
 Peligrad, C., (1986). Compact derivations of nest algebras. Proc. AMS 97, 668-672.
 
 

Gootman, E., Lazar, A., & Peligrad, C., (1994). Spectra for compact group actions.  J. Operator Theory,  31,  381-399.

Osterburg, J., & Peligrad, C., (1991). A strong Connes spectrum for finite group actions of simple rings.Journal of Algebra, 142, 424-434.

 Peligrad, C., (1992). Compact actions commuting with ergodic actions and applications to cross-products.Trans. Amer. Math. Soc. 331, pp. 825-836.  
 

 Longo, R. and Peligrad, C. (1984).  Non-commutative topological dynamics and compact actions on C*-algebras, J. Functional. Analysis 58, 157-174
.

Peligrad, C., Rubinstein, S., (1984). Maximal subalgebras of C*-crossed products. Pacific J. Math. 110, 325-335.
 
Peligrad, C., (1980) Reflexive operator algebras on non-commutative Hardy spaces. Math. Ann. 2253, 165-175. 
 
Christensen, E., & Peligrad, C., (1980). Commutants of nest algebras modulo the compact operators. Invent. Math. 56, 113-116.

 
 
 

Peligrad, C., (1981) Derivations of C*-algebras which are invariant under an automorphism group, OT Series Vol. 2, Birkhauser Verlag 
.

 Peligrad, C., (1982). Derivations of C*-algebras which are invariant under an automorphism group II. OT Series, Vol. 6, Birkhauser Verlag .
 
 Peligrad, C., (1979). Invariant subspaces of von Neumann algebras II. Proc. Amer. Math. Soc. 73, 346-350.
 
 Peligrad, C., (1979). On operators with reductive commutant and commutants of reductive operators. Rev. Roum. Math. Pures et Appl. 24, 153-159.

 

Peligrad, C., Duality and ergodic actions of simple Lie groups on operator algebras, Rocky Mountain J. Math., 29 (1990), p. 503-510.
 
Peligrad, C., Actions of compact groups on C*-algebras, Proceedings of Symposia in Pure Mathematics, Operator Theory/Operator Algebras, 51 (1990), 243-246.
 
Peligrad, C., Crossed product C*-algebras by compact group actions vs. fixed point algebras, Proceedings of GPOTS, Indianapolis, (1991), pp. 93-97.
 
 Peligrad, C., Reductive algebras which contain n-strictly cyclic algebras, Rev. Roum. Math. Pures et Appl. 19 (1974), 1041-1042.
 
Peligrad, C., Remarks on a theorem by R. G. Douglas and C. Pearcy, Rev. Roum. Math. Pure et Appl. 20 (1974), 1041-1043. 
.

 Peligrad, C. and Zsido, L., (1973). A Riesz decomposition theorem in W*-algebras, Acta. Sci. Math. (Szeged) 34, 317-322.  
 

 Peligrad, C., (1975). Invariant subspaces of von Neumann algebras. Acta Sci. Math. (Szeged) 37, 273-277. 

 Peligrad, C., (1974). On some transitive algebras. Rev. Roum. Math. Pures et Appl. 19, 245-250. 

Work in Progress

 

  1. Minimal and outer actions of compact groups on C*-algebras.
  2. Local limit theorems for psi-mixing Markov chains (with F. Merlevede and M. Peligrad)
  3. Quantum group actions on C*-algebras: spectra and ideal structure.
 
   

Presentations

Invited Presentations

Costel Peligrad (04-02-2017. ) A solution of the maximality problem for one-parameter dynamical systems .AMS Meeting #1127, Bloomington, Indiana. Professional Meeting. . Level:National

Costel Peligrad (03-23-2014. ) Minimal and outer actions of compact groups on operator algebras .University of Tennessee, Knoxville TN AMS Meeting # 1097, Knoxville TN. Professional Meeting. . Level:International

Costel Peligrad (03-22-2014. ) Reflexive operator algebras on non commutative Hardy spaces .University of Tennessee AMS Meeting #1097, Knoxville TN. Professional Meeting. . Level:International

(04-30-2013. ) Outer actions and co actions of compact groups on operator algebras .University of Rome, TorVergata,

F. Merlevede, C. Peligrad, M. Peligrad* (03-20-2013. ) The universality of spectral limit for random matrices with martingale differences entries. .1092 AMS meeting 2013 Louisville, KY, Louisville, KY. Professional Meeting. . Level:International

C. Peligrad, L. Zsido* (01-20-2012. ) Maximality of the algebra of analytic elements .ICMS Edinburgh, Scotland, Lancaster University, Edinburgh. Professional Meeting. . Level:International

M. Longla*, C. Peligrad, M. Peligrad (01-20-2013. ) On Functional CLT for reversible Markov chains with nonlinear growth of the variance of partial sums. 1092 AMS meeting 2013, San Diego .San Diego, CA, Professional Meeting. . Level:International

(03-2005. ) Unbounded derivations commuting with compact quantum group actions .University of Rome, Tor Vergata.

(2004. ) Maximal sub-algebras associated with C*-dynamical systems .20th Conference on Operator Theory, Timisoara, Romania.

(08-2003. ) Comparison of hereditary subalgebras of C*-algebras .UPR, Rio Piedras, Puerto Rico.

(06-1998. ) Open projections of C*-algebras .Timisoara, Romania.

(04-1997. ) A comparison of open projections .Univ. of Puerto Rico,

(03-1997. ) Strongly prime C*-algebras .Univ. of Puerto Rico,

(03-1995. ) Simple cross products of C*-algebras by coactions of compact matrix pseudogroups .Univ. of Rome,

(03-1995. ) Strongly prime C*-algebras .University of Tel Aviv,

(06-1993. ) Maximal subalgebras associated with one parameter C*-dynamical systems .Univ. of Rome, Torvergata.

(05-1993. ) Saturated actions of compact quantum groups on C*-algebras .Technion, Haifa, Israel.

(05-1993. ) Cross product C*-algebras by Hopf *-algebra actions .Univ. of Rome,

(04-1993. ) Analytic algebras associated with periodic C*-dynamical systems .Univ. of Puerto Rico, Mayaguez.

(03-1993. ) Actions of Hopf *-algebras on C*-algebras .Univ. of Puerto Rico, Rio Piedres.

(1991. ) Index of fixed point algebras for finite group actions .GPOTS, Texas A&M University, College Station, TX.

(06-1990. ) Connes spectrum for group actions .Predeal, Romania,

(1990. ) Spectra for compact group actions .GPOTS, University of New Mexico, Albuquerque, NM.

(05-1989. ) Maximality of analytic operator algebras associated with periodic flows .GPOTS, University of Houston.

(03-1989. ) Connes spectrum for compact nonabelian group actions .Southeastern Analysis Meeting, University of Georgia, Athens, GA.

(05-1988. ) Crossed products C*-algebras by compact group actions .GPOTS, Indianapolis, IN.

(10-1987. ) Duality and ergodic actions of simple Lie groups on operator algebra .837th Meeting of AMS, Special Session, Lincoln, NE.

(1987. ) Ergodic actions of simple Lie groups on operator algebras .GPOTS, UK, Lawrence.

(1986. ) Ergodic group actions and crossed products .Operator algebras, UC Santa Barbara.

(1985. ) Crossed product C*-algebras by compact group actions .GPOTS, Texas A&M University.

(1985. ) Prime and simple crossed products .Operator Algebras and Math Physics Conference, Iowa City.

(1985. ) Ergodic actions commuting with compact action .Optimization and Operator Theory, Lincoln, Nebraska.

(1984. ) Non commutative topological dynamics .Annual Meeting AMS, Louisville.

(1982. ) Unbounded derivations of C*-algebras .Operator Algebras Seminar, Rome.

(1979. ) Reflexive algebras on non commutative Hardy Spaces .Annual Conference on Functional Analysis, Prague.

(1977. ) Invariant subspaces of operator algebras .Banach Center, Warsaw.

(1974. ) Invariant subspaces of von Neumann algebras .Seminar of Functional Analysis, Steklov Math. Inst., Moscow.

Lecture

(03-20-2014. ) Reflexive Operator Algebras .UC. Level:Department

Event Organized

Great Plains Operator Theory Seminar

Great Plains Operator Theory Seminar Symposium 06-17-2008 06-22-2008 University of Cincinnati Level:International

AMS Sectional Meeting Special Sessions: Special Session on Recent Results on Operator Algebras

AMS Sectional Meeting Special Sessions: Special Session on Recent Results on Operator Algebras Prof. Meeting 10-21-2006 10-22-2006 University of Cincinnati Level:National

Great Plains Operator Theory Symposium

Great Plains Operator Theory Symposium Symposium 06-18-1995 06-22-1995 University of Cincinnati Level:International

Service

Taft Research Center (Taft Lecture ) Committee Chair Type:Departmental Service Level:Department 08-20-2013 -08-20-2016

(Barnett Lecture ) Committee Chair Type:Departmental Service Level:Department 08-20-2013 -08-20-2016

(Putnam and Virginia Tech Math Competitions ) Committee Member Type:Departmental Service Level:Department 09-29-2913 -12-20-2013

(Analysis preliminary exam ) Member Type:Departmental Service Level:Department 08-20-2013 -08-20-2020

Department of Mathematical Sciences (Math. Bowl ) Member Type:Departmental Service Level:Department 03-12-2014

Department of mathematcal Sciences (Seminar of Functional Analysis ) Committee Chair Type:Departmental Service Level:Department 08-01-2014 -05-01-2018

(RPT ) Member Type:Departmental Service Level:Department 08-01-2015 -08-01-2018

(Qualifier Examination ) Committee Member Type:Departmental Service Level:Department 08-01-2014 -08-01-2019

Courses Taught

15-MATH-409 INTRO ANALYSIS II Level:Undergraduate

INTRO TO ANALYSIS I Level:Undergraduate

15-MATH-252 CALCULUS II HONORS Level:Undergraduate

15-MATH-252 CALCULUS II Level:Undergraduate

15-MATH-351 LINEAR ALGEBRA I Level:Undergraduate

INTRO TO ANALYSIS Level:Undergraduate

DIFFERENTIAL EQUATIONS Level:Undergraduate

Introduction to Abstract Mathematics Level:Undergraduate

Introduction to Analysis Level:Undergraduate

MATH3001: INTRO ABST MATH (001) Level:Undergraduate

MATH1062-012: (15SS) CALCULUS II Level:Undergraduate

MATH9051: (15FS) SEMINAR FUNCT ANAL

MATH3002: (15FS) INTRO ANALYSIS (001) Level:Undergraduate