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.

- Crossed products and C*-covers of semi-Dirichlet operator algebras
(with A. Humeniuk and C. Ramsey),
*manuscript*(pdf file ) - Fell's absorption principle for semigroup operator algebras,
*Journal of NonCommutative Geometry, accepted*(pdf file ) - Stable isomorphisms of operator algebras (with E. Kakariadis and X. Li),
*International Mathematics Research Notices, accepted.*(pdf file ) - 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 ) - 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 ) - 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 ) - 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 ) - 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 ) - Product systems of C*-correspondences and Takai duality,
*Israel Journal of Mathematics 240 (2020), 223-251.*(pdf file ) - Operator algebras of higher rank numerical semigroups (with E. Kakariadis and X. Li),
*Proc. Amer. Math. Soc. 148 (2020), 4423-4433.*(pdf file ) - Tensor algebras of product systems and their C*-envelopes (with A. Dor-On),
*Journal of Functional Analysis 278 (2020), 108416.*(pdf file ) - The hyperrigidity of tensor algebras of C*-correspondences (with C. Ramsey),
*J. Math. Anal. Appl. 483 (2020), no. 1, 123611.*(pdf file ) - 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 ) - Crossed products of operator algebras: applications of Takai duality (with C. Ramsey),
*Journal of Functional Analysis 275 (2018), 1173-1207,*(pdf file ) - Pointwise conjugacy for multivariable dynamics over the Jacobson spectrum of a C*-algebra,
*Houston J. Math 44 (2018), 603-606.*(pdf file ) - 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 ) - 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 ) - C*-envelopes and the Hao-Ng isomorphism for discrete groups,
*International Mathematics Research Notices, Volume 2017, Issue 18 (2017), 5751-5768*. (pdf file ) - Limit algebras and integer valued cocycles, revisited (with C. Ramsey),
*Journal of the London Mathematical Society 94 (2016), 839-858.*(pdf file ) - Local maps and the representation theory of operator algebras,
*Transactions of the American Mathematical Society 368 (2016), 5377-5397.*(pdf file ) - The reflexive closure of the adjointable operators,
*Illinois Journal of Mathematics 58 (2014), 359-367.*(pdf file ) -
Isomorphism invariants for multivariable C*-dynamics (with E. Kakariadis),
*Journal of Non-Commutative Geometry 8 (2014), 771-787.*(pdf file ) -
Operator algebras and C*-correspondences: A survey (with E. Kakariadis),
*Operator Theory: Advances and Applications, Volume 233 (2014), 45-73.*( pdf file ) - C*-algebras and equivalences for C*-correspondences
(with E. Kakariadis),
*Journal of Functional Analysis 266 (2014), 956-988.*( pdf file ) -
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 ) -
Semicrossed products of the disc algebra (with K. Davidson),
*Proc. Amer. Math. Soc. 140 (2012), 3479-3484.*( pdf file ) -
Semicrossed products of operator algebras and their C*-envelopes (with E. Kakariadis),
*J. Funct. Anal. 262 (2012), 3108-3124.*( pdf file ) -
Dilation theory, commutant lifting and semicrossed products (with K. Davidson),
*Documenta Mathematika 16 (2011), 781-868.*( pdf file ) -
Operator algebras for multivariable dynamics (with K. Davidson),
*Memoirs of the American Mathematical Society 209, (2011), no 983.*( pdf file ) -
Dilating covariant representations of the non-commutative disc algebras (with K. Davidson),
*Journal of Functional Analysis 259, (2010), 817-831.*( pdf file ) -
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 ) -
Nonself-adjoint operator algebras for dynamical systems (with K. Davidson),
*Operator structures and dynamical systems, Contemp. Math. 503, (2009), 39-51.*( pdf file ) -
Semicrossed products of simple C*-algebras (with K. Davidson),
*Math. Ann. 342 (2008), 515-525*. ( pdf file ) -
Isomorphisms between topological conjugacy algebras (with K. Davidson),
*J. Reine Angew. Math. 621 (2008), 29-51*. ( pdf file ) -
Compact operators and nest representations of limit algebras
(with J. Peters),
*Trans. Amer. Math. Soc. 359 (2007), 2721-2739*. ( pdf file ) -
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 ) -
Nest representations of directed graph algebras, (with K. Davidson),
*Proc. London Math. Soc., 92, (2006), 762-790.*( pdf file ) -
Tensor algebras of C*-correspondences and their C*-envelopes (with D. Kribs),
*Journal of Functional Analysis 234, (2006), 226-233.*( pdf file ) -
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 ) -
Isomorphisms of algebras associated with directed graphs, (with D. Kribs),
*Math. Ann. 330, (2004), 709-728.*( pdf file ) -
Geometry of the Unit Ball and Representation Theory for Operator Algebras,
*Pacific J. Math., 216, (2004), 267-292.*( pdf file ) -
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 ) -
Primitive Limit Algebras and C*-Envelopes,
*Advances in Math.*170, (2002), 181-205, (with K. R. Davidson). ( pdf file ) -
The Structure of Free Semigroup Algebras,
*J. Reine Angew. Math.*533, (2001), 99-125, (with K. R. Davidson and D. R. Pitts). ( pdf file ) -
Algebraic Isomorphisms of Limit Algebras,
*Trans. Amer. Math. Soc.*353(3), (2001), 1169-1182, (with A. P. Donsig and T. D. Hudson). -
Primitive Triangular UHF Algebras,
*Journal of Functional Analysis*, 160, (1998), 1-27, (with T. D. Hudson). -
Factorization in nest algebras II,
*Trans. Amer. Math. Soc.*350, (1998), 165-183, (with M. Anoussis). -
Compact Operators and the Geometric Structure of Nest Algebras,
*Indiana. Univ. Math. J.*46, (1997), 319-336 (with M. Anoussis). -
Extreme Points in Triangular UHF Algebras,
*Trans. Amer. Math. Soc.*349, (1997), 3391-3400, (with T. D. Hudson and D. R. Larson). -
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. -
Factorization in Nest Algebras,
*Proc. Amer. Math. Soc.*125, (1997), 87-92, (with M. Anoussis). -
Compact Operators and the Geometric Structure of C*-algebras,
*Proc. Amer. Math. Soc.*124, (1996), 2115-2122, (with M. Anoussis). -
A non-selfadjoint Russo-Dye Theorem,
*Math. Ann.*304, (1996), 685-699, (with M. Anoussis). ( pdf file ) -
Reflexivity for a Class of Subspace Lattices,
*Math. Proc. Cambridge Phil. Soc.*119, (1996), 67-71. -
Hilbert-Schmidt and Finite Rank Operators in CSL Algebras,
*J. Operator Theory*34 (1995), 307-314, (with M. Anoussis). -
Remarks on the Interpolation and the Similarity Problem for Nest Subalgebras
of von Neumann Algebras,
*J. Math. Anal. Appl.*190, (1995), 755-762. -
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). -
Compact Solutions to an Operator Equation in Nest and CSL Algebras,
*Indiana Univ. Math. J.*42, (1993), 283-294, (with M. Anoussis & S. Power). -
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). -
Complemented Subspaces of Cp Spaces and CSL Algebras,
*J. London Math. Soc.*45 (1992), 301-313, (with M. Anoussis). -
Compact Perturbations of Certain CSL Algebras,
*Proc. Amer. Math. Soc.*114 (1992) 1041--1044, (with S. C. Power). -
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). -
The Equation Tx = y in Nest Algebras,
*Contemporary Mathematics*120, (1991), 83-87. -
On Compact Operators in Certain Reflexive Operator Algebras,
*J. Operator Theory*25, (1991), 177-182, (with R. L. Moore). -
Semisimplicity in Operator Algebras and Subspace Lattices,
*J. London Math. Soc.*42, (1990), 365-372 (with A. Katavolos). -
Descriptions of Nest Algebras,
*Proc. Amer. Math. Soc.*109, (1990), 739-745, (with M. Anoussis). -
Integration with Respect to a Commutative Subspace Lattice,
*J. Operator Theory*22 (1989), 307-322.