Advances in Operator Theory

$k$th-order slant Toeplitz operators on the Fock space

Shivam Kumar Kumar Singh and Anuradha Gupta

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Abstract

The notion of slant Toeplitz operators $B_\phi$ and $k$th-order slant Toeplitz operators $B_\phi^k$ on  the Fock space is introduced and some of its properties are investigated. The  Berezin transform of slant Toeplitz operator $B_\phi$ is also obtained. In addition, the commutativity of $k$th-order slant Toeplitz operators with co-analytic and harmonic symbols is discussed.

Article information

Source
Adv. Oper. Theory, Volume 2, Number 3 (2017), 318-333.

Dates
Received: 2 March 2017
Accepted: 19 May 2017
First available in Project Euclid: 4 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.aot/1512431679

Digital Object Identifier
doi:10.22034/aot.1703-1133

Mathematical Reviews number (MathSciNet)
MR3730057

Zentralblatt MATH identifier
06770929

Subjects
Primary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
Secondary: 46E20: Hilbert spaces of continuous, differentiable or analytic functions

Keywords
$k$th-order slant Toeplitz operator Fock space Berezin transform

Citation

Singh, Shivam Kumar Kumar; Gupta, Anuradha. $k$th-order slant Toeplitz operators on the Fock space. Adv. Oper. Theory 2 (2017), no. 3, 318--333. doi:10.22034/aot.1703-1133. https://projecteuclid.org/euclid.aot/1512431679


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