Generalizations of some classical theorems to D-normal operators on Hilbert spaces-Reference-Cited by-同舟云学术

Generalizations of some classical theorems to D-normal operators on Hilbert spaces

Published:2020-04-15 Issue:1 Volume:2020 Page:
ISSN:1029-242X
Container-title:Journal of Inequalities and Applications
language:en
Short-container-title:J Inequal Appl

Author:

Dana M.,Yousefi R.

Abstract

AbstractWe say that a Drazin invertible operator T on Hilbert space is of class

$[DN]$

[DN] if

$T^{D}T^{*} = T^{*}T^{D}$

TDT∗=T∗TD. The authors in (Oper. Matrices 12(2):465–487, 2018) studied several properties of this class. We prove the Fuglede–Putnam commutativity theorem for D-normal operators. Also, we show that T has the Bishop property

$(\beta)$

(β). Finally, we generalize a very famous result on products of normal operators due to I. Kaplansky to D-normal matrices.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

Link

https://link.springer.com/content/pdf/10.1186/s13660-020-02367-z.pdf

Reference14 articles.

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