Aequationes Mathematicae, ( ISI ), Volume (94), No (5), Year (2020-10) , Pages (979-987)

Title : ( Approximate n-idempotents and generalized Aluthge transform )

Authors: Mohammad Sal Moslehian ,

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‎In this note‎, ‎we remark that if $p\\\\\\\\neq 1$‎, ‎then $T$ is an $n$-idempotent‎. ‎If‎ ‎$p=1$‎, ‎the operator $T$ is a self-adjoint contraction satisfying $(-T)^n\\\\\\\\geq 0$‎, ‎and $\\\\\\\\varepsilon< \\\\\\\\frac{n-1}{n\\\\\\\\,\\\\\\\\sqrt[n-1]{n}}$‎, ‎then there is a self-adjoint $n$-idempotent $S$ such that‎ ‎$\\\\\\\\|T-S\\\\\\\\| < K\\\\\\\\varepsilon$ for some constant $K>0$‎. ‎Among other results‎, ‎we examine the lack of a similar result for the $(1,\\\\\\\\varepsilon)$-approximate generalized Aluthge transform‎.


, ‎Generalized Aluthge transform; $n$, idempotent; quasinormal operator; stability
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author = {Sal Moslehian, Mohammad},
title = {Approximate n-idempotents and generalized Aluthge transform},
journal = {Aequationes Mathematicae},
year = {2020},
volume = {94},
number = {5},
month = {October},
issn = {0001-9054},
pages = {979--987},
numpages = {8},
keywords = {‎Generalized Aluthge transform; $n$-idempotent; quasinormal operator; stability},


%0 Journal Article
%T Approximate n-idempotents and generalized Aluthge transform
%A Sal Moslehian, Mohammad
%J Aequationes Mathematicae
%@ 0001-9054
%D 2020