# 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 language English 597-610 14 Mathematical Inequalities and Applications 23 2 https://doi.org/10.7153/mia-2020-23-49 Published - Apr 2020

## Keywords

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

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