My research interests are in the fields of Operator Theory and Operator Algebras. More specifically, I am interested in Toeplitz, Hankel, composition operators, weighted composition operators on Hilbert spaces of analytic function spaces such as Bergman, Hardy and Segal-Bargmann (Fock) spaces. I am also interested in dilation theory, frame theory and its applications, and reproducing kernel methods in Machine Learning.

The posted version of my published papers below may be slightly different from the publishers' versions. Click a title to see the coressponding abstract. Click an abstract to hide it.

- On compactness of products of Toeplitz operators (pdf) (with Tomas Miguel Rodriguez and Sonmez Sahutoglu), submitted (2024), ;
__arXiv:2401.04869__ - Closed-range posinormal operators and their products (pdf) (with Paul Bourdon, Carlos Kubrusly and Derek Thompson), Linear Algebra Appl. 671 (2023), 38--58;
__arXiv:2212.02012__ - Spectra of some weighted composition operators on the ball (pdf) (with Scott Kaschner, Chloe Makdad, Benjamin Rempfer, Derek Thompson and DeJuan Winters), Acta Sci. Math. (Szeged) (2023),
- Square roots of weighted shifts of multiplicity two (pdf) (with Chanaka Kottegoda and Tomas Miguel Rodriguez), Canadian Mathematical Bull. (2022),
- A generalization of the Brown-Halmos theorems for the unit ball (pdf) (with Akaki Tikaradze), Adv. Math. 404 (2022), Paper No. 108411;
__arXiv:2101.03937__ - Analogues of finite Blaschke products as inner functions (pdf) (with Christopher Felder), Bull. Lond. Math. Soc. (2022), 1--20;
__arXiv:2105.01766__

- On compactness of products of Toeplitz operators (pdf) (with Tomas Miguel Rodriguez and Sonmez Sahutoglu), submitted (2024), ;
__arXiv:2401.04869__ - Closed-range posinormal operators and their products (pdf) (with Paul Bourdon, Carlos Kubrusly and Derek Thompson), Linear Algebra Appl. 671 (2023), 38--58;
__arXiv:2212.02012__ - Spectra of some weighted composition operators on the ball (pdf) (with Scott Kaschner, Chloe Makdad, Benjamin Rempfer, Derek Thompson and DeJuan Winters), Acta Sci. Math. (Szeged) (2023),
- Square roots of weighted shifts of multiplicity two (pdf) (with Chanaka Kottegoda and Tomas Miguel Rodriguez), Canadian Mathematical Bull. (2022),
- A generalization of the Brown-Halmos theorems for the unit ball (pdf) (with Akaki Tikaradze), Adv. Math. 404 (2022), Paper No. 108411;
__arXiv:2101.03937__ - Analogues of finite Blaschke products as inner functions (pdf) (with Christopher Felder), Bull. Lond. Math. Soc. (2022), 1--20;
__arXiv:2105.01766__ - Finite rank perturbations of Toeplitz products on the Bergman space (pdf) (with Damith Thilakarathna), J. Funct. Anal. 280 (2021), no. 7, 108850;
__arXiv:2011.05414__ - Hyponormal Toeplitz operators on weighted Bergman spaces (pdf) (with Brian Simanek), Integral Transforms Spec. Funct. 32 (2021), no. 5-8, 560-567;
__arXiv:2003.07330__ - Inner functions in weighted Hardy spaces (pdf), Anal. Math. Phys. 10 (2020), no. 2, Paper No. 25;
__arXiv:1912.05715__ - Decomposing algebraic $m$-isometric tuples (pdf), J. Funct. Anal. 278 (2020), no. 8, 108424;
__arXiv:1912.05954__ - Self-commutator norm of hyponormal Toeplitz operators (pdf), Oper. Matrices 13 (2019), no. 1, 85--91
- Coposinormality of the Cesàro matrices (pdf) (with H. C. Rhaly Jr.), Arch. Math. (Basel) 110 (2018), no. 2, 167--173
- Commutants of Toeplitz operators with harmonic symbols (pdf) (with Akaki Tikaradze), New York J. Math. 23 (2017), 1723--1731;
__arXiv:1706.01510__ - Composition operators on Hilbert spaces of entire functions of several variables (pdf) (with Minh Luan Doan and Le Hai Khoi), Integral Equations Operator Theory 88 (2017), no. 3, 301--330
- Commutants of separately radial Toeplitz operators in several variables (pdf), J. Math. Anal. Appl. 453 (2017), no. 1, 48--63
- Composition operators between Segal-Bargmann spaces (pdf), J. Operator Theory 78 (2017), no. 1, 135--158
- Composition operators between $\mathcal{N}_p$-spaces in the ball (pdf) (with Bingyang Hu and Le Hai Khoi), North-West. Eur. J. Math. 2 (2016), 103--120
- Adjoints of linear fractional composition operators on weighted Hardy spaces (pdf) (with Zeljko Cuckovic), Acta Sci. Math. (Szeged) 82 (2016), no. 3-4, 651--662;
__arXiv:1509.01510__ - The structure of $m$-isometric weighted shift operators (pdf) (with Belal Abdullah), Oper. Matrices 10 (2016), no. 2, 319--334
- Commutants of Toeplitz operators with separately radial polynomial symbols (pdf) (with Amila Appuhamy), Complex Anal. Oper. Theory 10 (2016), no. 1, 1--12
- Algebraic properties of operator roots of polynomials (pdf), J. Math. Anal. Appl. 421 (2015), no. 2, 1238--1246
- Invertible composition operators: the product of a composition operator with the adjoint of a composition operator (pdf) (with John H. Clifford and Alan Wiggins), Complex Anal. Oper. Theory 8 (2014), no. 8, 1699--1706
- Normal and isometric weighted composition operators on the Fock space (pdf), Bull. Lond. Math. Soc. 46 (2014), no. 4, 847--856
- Hilbert-Schmidt Hankel operators over complete Reinhardt domains (pdf), Integral Equations Operator Theory 78 (2014), no. 4, 515--522
- Toeplitzness of composition operators in several variables (pdf) (with Zeljko Cuckovic), Complex Var. Elliptic Equ. 59 (2014), no. 10, 1351--1362;
__arXiv:1308.2214__ - Toeplitz operators on Bergman spaces of polyanalytic functions (pdf) (with Zeljko Cuckovic), Bull. Lond. Math. Soc. 44 (2012), no. 5, 961--973;
__arXiv:1012.2816__ - Toeplitz operators on radially weighted harmonic Bergman spaces (pdf), J. Math. Anal. Appl. 396 (2012), no. 1, 164--172;
__arXiv:1004.0860__ - Self-adjoint, unitary, and normal weighted composition operators in several variables (pdf), J. Math. Anal. Appl. 395 (2012), no. 2, 596--607;
__arXiv:1207.5980__ - Algebraic properties and the finite rank problem for Toeplitz operators on the Segal-Bargmann space (pdf) (with Wolfram Bauer), J. Funct. Anal. 261 (2011), no. 9, 2617--2640
- Compact Toeplitz operators on Segal-Bargmann type spaces (pdf) (with Bo Li), New York J. Math. 17A (2011), 213--224
- Commutator ideals of subalgebras of Toeplitz algebras on weighted Bergman spaces (pdf), J. Operator Theory 64 (2010), no. 1, 89--101
- Compact Hankel operators on generalized Bergman spaces of the polydisc (pdf), Integral Equations Operator Theory 67 (2010), no. 3, 425--438
- A refined Luecking's theorem and finite-rank products of Toeplitz operators (pdf), Complex Anal. Oper. Theory 4 (2010), no. 2, 391--399;
__arXiv:0802.3925__ - Commutant lifting for commuting row contractions (pdf) (with Kenneth R. Davidson), Bull. Lond. Math. Soc. 42 (2010), no. 3, 506--516;
__arXiv:0906.4526__ - On Toeplitz operators on Bergman spaces of the unit polydisk (pdf), Proc. Amer. Math. Soc. 138 (2010), no. 1, 275--285
- Compact Toeplitz operators with continuous symbols (pdf), Glasg. Math. J. 51 (2009), no. 2, 257--261
- Finite-rank products of Toeplitz operators in several complex variables (pdf), Integral Equations Operator Theory 63 (2009), no. 4, 547--555
- The commutants of certain Toeplitz operators on weighted Bergman spaces (pdf), J. Math. Anal. Appl. 348 (2008), no. 1, 1--11;
__arXiv:0802.3921__ - On the commutator ideal of the Toeplitz algebra on the Bergman space of the unit ball in $\mathbb{C}^n$ (pdf), J. Operator Theory 60 (2008), no. 1, 149--163
- On a class of ideals of the Toeplitz algebra on the Bergman space (pdf), Proc. Amer. Math. Soc. 136 (2008), no. 10, 3571--3577;
__arXiv:0705.0970__ - On the essential commutant of Toeplitz operators in several complex variables (pdf), Integral Equations Operator Theory 59 (2007), no. 4, 555--578

- Finite rank Toeplitz operators (pdf), 2013. In this note we offer a simplified proof of a theorem by Borichev and Rozenblum on finite rank Toeplitz operators whose symbols may have unbounded supports.
- Trace class Toeplitz operators with unbounded symbols on weighted Bergman spaces (pdf), 2010. In this note we give an easy construction of functions on the unit ball that are not essentially bounded near any point on the unit sphere but the corresponding Toeplitz operators are all trace class on the Bergman space.
- Commutator ideals of subalgebras of Toeplitz algebras on weighted Bergman spaces II (pdf), 2007. In this note we give a more general result than the result in our previous paper. The technique is almost the same as before.

This webpage uses the bootstrap framework.