MY PREPRINTS AND PUBLICATIONS

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 publisher's version.

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  1. Commutants of Toeplitz operators with harmonic symbols (pdf), with Akaki Tikaradze, 2017, submitted.
  2. Coposinormality of the Cesàro matrices (pdf), with H.C. Rhaly Jr., 2017, submitted.
  3. Composition operators on Hilbert spaces of entire functions of several variables (pdf), with M.L. Doan and L.H. Khoi, Integr. Equ. Oper. Theory 88 (2017), no.3, 301-330.
  4. Commutants of separately radial Toeplitz operators in several variables (pdf), J. Math. Anal. Appl. 453 (2017), no. 1, 48--63.
  5. Composition operators between Segal--Bargmann spaces (pdf), Journal of Operator Theory 78 (2017), no. 1, 135--158.
  6. Adjoints of linear fractional composition operators on weighted Hardy spaces (pdf) (with Zeljko Cuckovic) Acta Sci. Math. (Szeged) 82:3-4(2016), 651--662.
  7. The structure of $m$-isometric weighted shift operators (pdf) (with Belal Abdullah) Operators and Matrices 10 (2016), no. 2, 319--334.
  8. Essential norm for weighted composition operators on $\mathcal{N}_p$ spaces in the ball (pdf) (with Bingyang Hu and Le Hai Khoi) Vietnam J. Math. (2016) 44, 431--439.
  9. Commutants of Toeplitz operators with separately radial polynomial symbols (pdf) (with Amila Appuhamy) Complex Anal. Oper. Theory 10 (2016), no. 1, 1--12.
  10. Algebraic properties of operator roots of polynomials (pdf) J. Math. Anal. Appl. 421 (2015), no. 2, 1238--1246.
  11. Normal and isometric weighted composition operators on the Fock space (pdf) Bull. London Math. Soc. (2014) 46 (4), 847--856.
  12. Hilbert--Schmidt Hankel operators over complete Reinhardt domains (pdf) Integr. Equ. Oper. Theory 78 (2014), no. 4, 515--522.
  13. Invertible composition operators: the product of a composition operator with the adjoint of a composition operator (pdf) (with John Clifford and Alan Wiggins) Complex Anal. Oper. Theory 8 (2014), no. 8, 1699--1706.
  14. Toeplitzness of composition operators in several variables (pdf) (with Zeljko Cuckovic) Complex Var. Elliptic Equ. 59 (2014), no. 10, 1351--1362.
  15. Self-adjoint, unitary, and normal weighted composition operators in several variables (pdf), J. Math. Anal. Appl. 395 (2012), 596--607.
  16. Algebraic properties and the finite rank problem for Toeplitz operators on the Segal-Bargmann space (pdf) (with Wolfram Bauer), Journal of Functional Analysis 261 (2011), 2617--2640.
  17. Toeplitz operators on Bergman spaces of polyanalytic functions (pdf) (with Zeljko Cuckovic), Bull. London Math. Soc. 44 (2012), no. 5, 961--973.
  18. Compact Toeplitz operators on Segal-Bargmann type spaces (pdf) (with Bo Li), New York Journal of Mathematics 17a (2011), 213--224.
  19. Toeplitz operators on radially weighted harmonic Bergman spaces (pdf), J. Math. Anal. Appl. 396 (2012), 164--172.
  20. Compact Hankel operators on generalized Bergman spaces of the polydisc (pdf), Integr. Equ. Oper. Theory 67 (2010), no. 3, 425--438.
  21. Commutant lifting for commuting row contractions (pdf) (with Kenneth R. Davidson), Bull. London Math. Soc. 42 (2010), no. 3, 506--516.
  22. On Toeplitz operators on Bergman spaces of the unit polydisk (pdf), Proc. Amer. Math. Soc. 138 (2010), no. 1, 275--285.
  23. Commutator ideals of subalgebras of Toeplitz algebras on weighted Bergman spaces (pdf), Journal of Operator Theory 64 (2010), no. 1, 89--101.
  24. Finite-rank products of Toeplitz operators in several complex variables (pdf), Integr. Equ. Oper. Theory 63 (2009), no. 4, 547--555.
  25. A refined Luecking's theorem and finite-rank products of Toeplitz operators (pdf), Complex Anal. Oper. Theory 4 (2010), no. 2, 391--399.
  26. Compact Toeplitz operators with continuous symbols (pdf), Glasgow Mathematical Journal 51 (2009), no. 2, 257--261.
  27. The commutants of certain Toeplitz operators on weighted Bergman spaces (pdf), J. Math. Anal. Appl. 348 (2008), no. 1, 1--11.
  28. On the commutator ideal of the Toeplitz algebra on the Bergman space of the unit ball in \(\mathbf{C}^n\) (pdf), Journal of Operator Theory 60 (2008), no. 1, 149--163.
  29. On a class of ideals of the Toeplitz algebra on the Bergman space (pdf), Proc. Amer. Math. Soc. 136 (2008), no. 10, 3571--3577.
  30. On the essential commutant of Toeplitz operators in several complex variables (pdf), Integr. Equ. Oper. Theory 59 (2007), no. 4, 555--578.

Unpublished Notes

  1. 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.
  2. 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.
  3. Diagonal Toeplitz operators on weighted Bergman spaces (pdf), 2007. The main results in this paper are covered by the results in "The commutants of certain Toeplitz operators on weighted Bergman spaces" and "Finite-rank products of Toeplitz operators in several complex variables".
  4. 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.
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