Research Interests

My research interests are focused on operator algebras with an emphasis on the non-selfadjoint aspects of the theory. I am currently interested in various topics of investigation including: C*-envelope, non-selfadjoint crossed products, the classification problem for operator algebras and its relation with representation theory. Over the years, I have worked on various non-selfadjoint algebras such as tensor algebras, nest algebras, CSL algebras and triangular AF algebras, free semigroup algebras, graph algebras and semicrossed products. I am also interested in Banach spaces and their isometric theory (extreme points, M-ideals, etc.)

See here a photo of several non-selfadjoint operator algebraists, including myself at the bottom-right. Here is another more dynamical photo. In 2010 I took this multivariate photo.

Publications

  1. Crossed products and C*-covers of semi-Dirichlet operator algebras (with A. Humeniuk and C. Ramsey), manuscript (pdf file )

  2. Fell's absorption principle for semigroup operator algebras, Journal of NonCommutative Geometry, accepted (pdf file )

  3. Stable isomorphisms of operator algebras (with E. Kakariadis and X. Li), International Mathematics Research Notices, accepted. (pdf file )

  4. Co-universality and controlled maps on product systems over right LCM-semigroups (with E. Kakariadis, M. Laca and X. Li), Analysis & PDE 16 (2023), no. 6, 1433?1483.. (pdf file )

  5. The isomorphism problem for tensor algebras of multivariable dynamical systems (with C. Ramsey), Forum of Mathematics, Sigma , Volume 10 , 2022 , e81 DOI: https://doi.org/10.1017/fms.2022.73 (pdf file )

  6. C*-envelopes for operator algebras with a coaction and co-universal C*-algebras for product systems (with A. Dor-On, E. Kakariadis, M. Laca and X. Li), Advances in Mathematics 400 (2022), Paper No. 108286. (pdf file )

  7. Boundary quotient C*-algebras of semigroups (with E. Kakariadis, M. Laca and X. Li), J. Londaon Math Soc., DOI: 10.1112/jlms.12557 (pdf file )

  8. The non-selfadjoint approach to the Hao-Ng isomorphism (with C. Ramsey), International Mathematics Research Notices, Vol. 2021, Issue 2, January 2021, Pages 1160-1197. (pdf file )

  9. Product systems of C*-correspondences and Takai duality, Israel Journal of Mathematics 240 (2020), 223-251. (pdf file )

  10. Operator algebras of higher rank numerical semigroups (with E. Kakariadis and X. Li), Proc. Amer. Math. Soc. 148 (2020), 4423-4433. (pdf file )

  11. Tensor algebras of product systems and their C*-envelopes (with A. Dor-On), Journal of Functional Analysis 278 (2020), 108416. (pdf file )

  12. The hyperrigidity of tensor algebras of C*-correspondences (with C. Ramsey), J. Math. Anal. Appl. 483 (2020), no. 1, 123611. (pdf file )

  13. Crossed products of operator algebras (with C. Ramsey), Memoirs of the American Mathematical Society 258 (2019), Number 1240. ISBNs: 978-1-4704-3545-5 (print); 978-1-4704-5071-7 (online). (pdf file )

  14. Crossed products of operator algebras: applications of Takai duality (with C. Ramsey), Journal of Functional Analysis 275 (2018), 1173-1207, (pdf file )

  15. Pointwise conjugacy for multivariable dynamics over the Jacobson spectrum of a C*-algebra, Houston J. Math 44 (2018), 603-606. (pdf file )

  16. Non-selfadjoint operator algebras: dynamics, classification and C*-envelopes, expository article, chapter in Recent Advances in Operator Theory and Operator Algebras, CRC Press. (pdf file )

  17. Morita equivalence of C*-correspondences passes to the related operator algebras (with G. Eleftherakis and E. Kakariadis), Israel Journal of Mathematics 222 (2017), no. 2, 949-972. (pdf file )

  18. C*-envelopes and the Hao-Ng isomorphism for discrete groups, International Mathematics Research Notices, Volume 2017, Issue 18 (2017), 5751-5768 . (pdf file )

  19. Limit algebras and integer valued cocycles, revisited (with C. Ramsey), Journal of the London Mathematical Society 94 (2016), 839-858. (pdf file )

  20. Local maps and the representation theory of operator algebras, Transactions of the American Mathematical Society 368 (2016), 5377-5397. (pdf file )

  21. The reflexive closure of the adjointable operators, Illinois Journal of Mathematics 58 (2014), 359-367. (pdf file )

  22. Isomorphism invariants for multivariable C*-dynamics (with E. Kakariadis), Journal of Non-Commutative Geometry 8 (2014), 771-787. (pdf file )

  23. Operator algebras and C*-correspondences: A survey (with E. Kakariadis), Operator Theory: Advances and Applications, Volume 233 (2014), 45-73. ( pdf file )

  24. C*-algebras and equivalences for C*-correspondences (with E. Kakariadis), Journal of Functional Analysis 266 (2014), 956-988. ( pdf file )

  25. Contributions to the theory of C*-correspondences with applications to multivariable dynamics (with E. Kakariadis), Transactions of the American Mathematical Society 364 (2012), 6605-6630. ( pdf file )

  26. Semicrossed products of the disc algebra (with K. Davidson), Proc. Amer. Math. Soc. 140 (2012), 3479-3484. ( pdf file )

  27. Semicrossed products of operator algebras and their C*-envelopes (with E. Kakariadis), J. Funct. Anal. 262 (2012), 3108-3124. ( pdf file )

  28. Dilation theory, commutant lifting and semicrossed products (with K. Davidson), Documenta Mathematika 16 (2011), 781-868. ( pdf file )

  29. Operator algebras for multivariable dynamics (with K. Davidson), Memoirs of the American Mathematical Society 209, (2011), no 983. ( pdf file )

  30. Dilating covariant representations of the non-commutative disc algebras (with K. Davidson), Journal of Functional Analysis 259, (2010), 817-831. ( pdf file )

  31. Biholomorphisms of the unit ball of C^n and semicrossed products (with K. Davidson), Operator Theory Live, Timisoara, July 3-8, 2008, Theta Series in Advanced Mathematics (2010), 69-80. ( pdf file )

  32. Nonself-adjoint operator algebras for dynamical systems (with K. Davidson), Operator structures and dynamical systems, Contemp. Math. 503, (2009), 39-51. ( pdf file )

  33. Semicrossed products of simple C*-algebras (with K. Davidson), Math. Ann. 342 (2008), 515-525. ( pdf file )

  34. Isomorphisms between topological conjugacy algebras (with K. Davidson), J. Reine Angew. Math. 621 (2008), 29-51. ( pdf file )

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

  36. 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 )

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

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

  39. 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 )

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

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

  42. 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 )

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

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

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

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

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

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

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

  50. 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.

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

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

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

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

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

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

  57. 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).

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

  59. 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).

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

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

  62. 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).

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

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

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

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

  67. 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