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

2 Scopus citations

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

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© 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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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.",

keywords = "Duggal transform, Invariant subspaces, Polar decomposition, Weighted mean transform",

author = "Sungeun Jung and Eungil Ko and Lee, \{Mee Jung\}",

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T1 - On the iterated mean transforms of operators

AU - Jung, Sungeun

AU - Ko, Eungil

AU - Lee, Mee Jung

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N2 - 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.

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.

KW - Duggal transform

KW - Invariant subspaces

KW - Polar decomposition

KW - Weighted mean transform

UR - https://www.scopus.com/pages/publications/85092766932

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DO - 10.7153/mia-2020-23-49

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VL - 23

SP - 597

EP - 610

JO - Mathematical Inequalities and Applications

JF - Mathematical Inequalities and Applications

IS - 2

ER -

On the iterated mean transforms of operators

Abstract

Bibliographical note

Keywords

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