Multivariate analogue of slant Toeplitz operators

Year 2021, Volume: 50 Issue: 3, 678 - 691, 07.06.2021

Gopal Datt Shesh Pandey

https://doi.org/10.15672/hujms.663262

Cited By: 1

Abstract

This paper discusses several structural and fundamental properties of the $k^{th}$-order slant Toeplitz operators on the Lebesgue space of the $n$- torus $\mathbb{T}^n$, for integers $k\geq 2$ and $n\geq 1$. We obtain certain equivalent conditions for the commutativity and essential commutativity of these operators. In the last section, we deal with the spectrum of a $k^{th}$-order slant Toeplitz operator on $L^2(\mathbb{T}^n)$ and investigate the conditions for such an operator to be an isometry, hyponormal or normal.

Keywords

commutativity, Lebesgue space, slant Toeplitz operators, n-dimensional torus

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