Pradeep, R (2021) ON m–QUASI–TOTALLY–(α,β)–NORMAL OPERATORS. Operators and Matrices, 15 (3). pp. 1-2. ISSN 1055–1072

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Abstract

An operator S acting on a Hilbert space is called m-quasi-totally-(α,β)-normal
(0 α 1 β) if
α2S m∗(S −λ)
∗(S −λ)S m S m∗(S −λ)(S −λ)
∗S m β2S m∗(S −λ)
∗(S −λ)S m
for a natural number m and for all λ ∈ C. m-quasi-totally-(α,β)-normal operator is equivalent
to the study of mutual majorization between (S − λ)S m and (S − λ)∗S m for a natural
number m and for all λ ∈ C. This article aims to establish various inequalities between the
operator norm and the numerical radius of m-quasi-totally-(α,β)-normal operators in Hilbert
spaces. Further, this article analyzes spectral and algebraic properties of m-quasi-totally-(α,β)-
normal operators.
Mathematics subject classification (2020): 47B15, 47B20, 47A15.

Item Type: Article
Uncontrolled Keywords: m-quasi-totally-(α,β)-normal operators, mutual majorization, numerical radius, operator norm, single valued extension property
Divisions: PSG College of Arts and Science > Department of Mathematics
Depositing User: Mr Team Mosys
Date Deposited: 23 Jun 2022 03:02
Last Modified: 23 Jun 2022 03:02
URI: http://ir.psgcas.ac.in/id/eprint/1251

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