On the iterated mean transforms of operators

Sungeun Jung; Eungil Ko; Mee Jung Lee

doi:10.7153/mia-2020-23-49

On the iterated mean transforms of operators

Sungeun Jung, Eungil Ko, Mee Jung Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let T = U|T| be the polar decomposition of an operator T ϵ L(H ). For given s,t ≥ 0, we say that Ts,t:= sU|T|+t|T|U is the weighted mean transform of T . In this paper, we study properties of the k -th iterated weighted mean transform T^(k)_s,tof T = U|T| when U is unitary. In particular, we give the polar decomposition of such T^(k)_s,tand investigate its applications. Finally, we consider the iterated weighted mean transforms of a weighted shift.

Original language	English
Pages (from-to)	597-610
Number of pages	14
Journal	Mathematical Inequalities and Applications
Volume	23
Issue number	2
DOIs	https://doi.org/10.7153/mia-2020-23-49
State	Published - Apr 2020

Bibliographical note

Publisher Copyright:
© 2020 Element D.O.O.. All rights reserved.

Keywords

Duggal transform
Invariant subspaces
Polar decomposition
Weighted mean transform

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10.7153/mia-2020-23-49

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AB - Let T = U|T| be the polar decomposition of an operator T ϵ L(H ). For given s,t ≥ 0, we say that Ts,t:= sU|T|+t|T|U is the weighted mean transform of T . In this paper, we study properties of the k -th iterated weighted mean transform T(k)s,tof T = U|T| when U is unitary. In particular, we give the polar decomposition of such T(k)s,tand investigate its applications. Finally, we consider the iterated weighted mean transforms of a weighted shift.

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KW - Weighted mean transform

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On the iterated mean transforms of operators

Abstract

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Keywords

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