@article{e97ba82384214ef4bacc2e998bee5f8d,

title = "On the iterated mean transforms of operators",

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}",

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: {\textcopyright} 2020 Element D.O.O.. All rights reserved.",

year = "2020",

month = apr,

doi = "10.7153/mia-2020-23-49",

language = "English",

volume = "23",

pages = "597--610",

journal = "Mathematical Inequalities and Applications",

issn = "1331-4343",

publisher = "Element d.o.o.",

number = "2",

}