Costel Peligrad

Costel Peligrad

Professor

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

On the local limit theorems for psi-mixing Markov chains (with F. Merlevede and M. Peligrad), ALEA, Lat. Am. J. Probab. Math. Stat. 18 (2), 1221–1239 (2021).

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.

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.

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.

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. (with F. Merlevede and M.Peligrad) Local limit theorems for psi-mixing Markov chains.
  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

Chair of two Dissertation committees: Wojciech Szymanski (1994) and Raluca Dumitru (2007). Type:Departmental Service Level:Department