Title : ( Approximate n-idempotents and generalized Aluthge transform )
Authors: Mohammad Sal Moslehian ,Access to full-text not allowed by authors
Abstract
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.
Keywords
, Generalized Aluthge transform; $n$, idempotent; quasinormal operator; stability@article{paperid:1078908,
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