Trieu Le

The commutants of certain Toeplitz operators on weighted Bergman spaces

Abstract For α > − 1 , let A α 2 be the corresponding weighted Bergman space of the unit ball in C n . For a bounded measurable function f, let T f be the Toeplitz operator with symbol f on A α 2 . This paper describes all the functions f for which T f commutes with a given T g , where g ( z ) = z 1 L 1 ⋯ z n L n for strictly positive integers L 1 , … , L n , or g ( z ) = | z 1 | s 1 ⋯ | z n | s n h ( | z | ) for non-negative real numbers s 1 , … , s n and a bounded measurable function h on [ 0 , 1 ) .

Self-adjoint, unitary, and normal weighted composition operators in several variables

Abstract We study weighted composition operators on Hilbert spaces of analytic functions on the unit ball with kernels of the form ( 1 − 〈 z , w 〉 ) − γ for γ > 0 . We find necessary and sufficient conditions for the adjoint of a weighted composition operator to be a weighted composition operator or the inverse of a weighted composition operator. We then obtain characterizations of self-adjoint and unitary weighted composition operators. Normality of these operators is also investigated.

Toeplitz operators on Bergman spaces of polyanalytic functions

We study algebraic properties of Toeplitz operators on Bergman spaces of polyanalytic functions on the unit disk. We obtain results on finite-rank commutators and semi-commutators of Toeplitz operators with harmonic symbols. We also raise and discuss some open questions.

Commutant lifting for commuting row contractions

If

On Toeplitz operators on Bergman spaces of the unit polydisk

T= \big[ T_1 ... T_n\big]

COMPACT TOEPLITZ OPERATORS WITH CONTINUOUS SYMBOLS

is a row contraction with commuting entries, and the Arveson dilation is

Toeplitzness of composition operators in several variables

\tilde T= \big[ \tilde T_1 ... \tilde T_n\big]

On the Structure of \(\mathcal {N}_{p}\)-Spaces in the Ball

, then any operator

Normal and isometric weighted composition operators on the Fock space

X

Algebraic properties and the finite rank problem for Toeplitz operators on the Segal–Bargmann space

commuting with each