Mathematical Analysis and its Contemporary Applications

Characterization of uniformly asymptotic S-Toeplitz and S-Hankel operators

https://doi.org/10.30495/maca.2023.1989709.1071
Volume 5, Issue 2
Summer 2023
Pages 17-28
Mathematical Analysis and its Contemporary Applications

Document Type : Original Article

Authors

Massoud Salehi Sarvestani 1
Massoud Amini 2

1 Department of Mathematics, Savadkooh Branch, Islamic Azad University, Savadkooh, Iran

2 Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Tarbiat Modares, Tehran, Iran

Abstract
In this paper,  we show that a shift operator on a separable Hilbert space with infinite multiplicity is strongly approximated by shift operators with finite multiplicities. Moreover, for an arbitrary shift operator $S$, we introduce the notion of an (asymptotic) $S$-Hankel operator and study its relation to the class of (asymptotic) $S$-Toeplitz operators.

Keywords

Generalized Shift operator
S-Toeplitz operator
S-Hankel operator
Hardy space
  • Receive Date 15 February 2023
  • Revise Date 21 April 2023
  • Accept Date 22 April 2023

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