On the iterated mean transforms of operators

Sungeun Jung, Eungil Ko, Mee Jung Lee

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)597-610
Number of pages14
JournalMathematical Inequalities and Applications
Volume23
Issue number2
DOIs
StatePublished - Apr 2020

Bibliographical note

Funding Information:
The first author was supported by Hankuk University of Foreign Studies Research Fund and was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (2014R1A1A2056642). The second author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (2016R1D1A1B03931937). The third author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(NRF-2018R1A6A3A01010648). ∗ Corresponding author.

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

Keywords

  • Duggal transform
  • Invariant subspaces
  • Polar decomposition
  • Weighted mean transform

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