Research Interests

My research interests are focused on operator algebras with an emphasis on the non-selfadjoint aspects of the theory. I have worked on various non-selfadjoint algebras such as nest algebras, CSL algebras and triangular AF algebras. Lately, I am interested in free semigroup algebras. Topics of investigation include the geometry of the unit ball, representation theory and isomorphic/epimorphic theory. I am also interested in Banach spaces and their isometric theory (extreme points, M-ideals, etc.). A more detailed description of my research is available here

See here a photo of several non-selfadjoint operator algebraists, including myself at the bottom-right. Here is another more recent photo.

Publications

  1. Operator algebras for multivariable dynamics (with K. Davidson), submitted. ( pdf file )

  2. Semicrossed products of simple C*-algebras (with K. Davidson), Math. Ann., accepted. ( pdf file )

  3. Isomorphisms between topological conjugacy algebras (with K. Davidson), J. Reine Angew. Math., accepted. ( pdf file )

  4. Compact operators and nest representations of limit algebras (with J. Peters), Trans. Amer. Math. Soc. 359 (2007), 2721-2739 . ( pdf file )

  5. The C*-envelope of the tensor algebra of a directed graph, (with D. Kribs), Integral Equations and Operator Theory 56, (2006), 401-414. ( pdf file )

  6. Nest representations of directed graph algebras, (with K. Davidson), Proc. London Math. Soc., 92, (2006), 762-790. ( pdf file )

  7. Tensor algebras of C*-correspondences and their C*-envelopes (with D. Kribs), Journal of Functional Analysis 234, (2006), 226-233. ( pdf file )

  8. Applications of the Wold decomposition to the study of row contractions associated with directed graphs, (with D. Kribs), Trans. Amer. Math. Soc. 357, (2005), 3739-3755. ( pdf file )

  9. Isomorphisms of algebras associated with directed graphs, (with D. Kribs), Math. Ann. 330, (2004), 709-728. ( pdf file )

  10. Geometry of the Unit Ball and Representation Theory for Operator Algebras, Pacific J. Math., 216, (2004), 267-292. ( pdf file )

  11. Meet Irreducible Ideals and Representations of Limit Algebras, Journal of Functional Analysis, 200, (2003), 23-30, (with K. R. Davidson and J. Peters). ( pdf file )

  12. Primitive Limit Algebras and C*-Envelopes, Advances in Math. 170, (2002), 181-205, (with K. R. Davidson). ( pdf file )

  13. The Structure of Free Semigroup Algebras, J. Reine Angew. Math. 533, (2001), 99-125, (with K. R. Davidson and D. R. Pitts). ( pdf file )

  14. Algebraic Isomorphisms of Limit Algebras, Trans. Amer. Math. Soc. 353(3), (2001), 1169-1182, (with A. P. Donsig and T. D. Hudson).

  15. Primitive Triangular UHF Algebras, Journal of Functional Analysis, 160, (1998), 1-27, (with T. D. Hudson).

  16. Factorization in nest algebras II, Trans. Amer. Math. Soc. 350, (1998), 165-183, (with M. Anoussis).

  17. Compact Operators and the Geometric Structure of Nest Algebras, Indiana. Univ. Math. J. 46, (1997), 319-336 (with M. Anoussis).

  18. Extreme Points in Triangular UHF Algebras, Trans. Amer. Math. Soc. 349, (1997), 3391-3400, (with T. D. Hudson and D. R. Larson).

  19. Geometric Aspects of the Theory of Nest Algebras, Operator algebras and applications (Samos, 1996), 245--254, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 495, Kluwer Acad. Publ., Dordrecht, 1997.

  20. Factorization in Nest Algebras, Proc. Amer. Math. Soc. 125, (1997), 87-92, (with M. Anoussis).

  21. Compact Operators and the Geometric Structure of C*-algebras, Proc. Amer. Math. Soc. 124, (1996), 2115-2122, (with M. Anoussis).

  22. A non-selfadjoint Russo-Dye Theorem, Math. Ann. 304, (1996), 685-699, (with M. Anoussis). ( pdf file )

  23. Reflexivity for a Class of Subspace Lattices, Math. Proc. Cambridge Phil. Soc. 119, (1996), 67-71.

  24. Hilbert-Schmidt and Finite Rank Operators in CSL Algebras, J. Operator Theory 34 (1995), 307-314, (with M. Anoussis).

  25. Remarks on the Interpolation and the Similarity Problem for Nest Subalgebras of von Neumann Algebras, J. Math. Anal. Appl. 190, (1995), 755-762.

  26. Interpolation in Nest Algebras and Applications to Operator Corona Theorems, J. Operator Theory 29, (1993), 115-123, (with M. Anoussis, R. L. Moore and T.T. Trent).

  27. Compact Solutions to an Operator Equation in Nest and CSL Algebras, Indiana Univ. Math. J. 42, (1993), 283-294, (with M. Anoussis & S. Power).

  28. Interpolation Problems for Hilbert-Schmidt Operators in Reflexive Algebras, Houston J. Math. 19, (1993), 63-73, (with M. Anoussis, R. L. Moore, and T. Trent).

  29. Complemented Subspaces of Cp Spaces and CSL Algebras, J. London Math. Soc. 45 (1992), 301-313, (with M. Anoussis).

  30. Compact Perturbations of Certain CSL Algebras, Proc. Amer. Math. Soc. 114 (1992) 1041--1044, (with S. C. Power).

  31. Interpolation Problems for Ideals in Nest Algebras, Math. Proc. Cambridge Phil. Soc. 111, (1992), 151-160, (with M. Anoussis, R. L. Moore, and T. Trent).

  32. The Equation Tx = y in Nest Algebras, Contemporary Mathematics 120, (1991), 83-87.

  33. On Compact Operators in Certain Reflexive Operator Algebras, J. Operator Theory 25, (1991), 177-182, (with R. L. Moore).

  34. Semisimplicity in Operator Algebras and Subspace Lattices, J. London Math. Soc. 42, (1990), 365-372 (with A. Katavolos).

  35. Descriptions of Nest Algebras, Proc. Amer. Math. Soc. 109, (1990), 739-745, (with M. Anoussis).

  36. Integration with Respect to a Commutative Subspace Lattice, J. Operator Theory 22 (1989), 307-322.

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Elias G. Katsoulis- katsoulise(at)ecu.edu