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Document Details
Document Type
:
Article In Journal
Document Title
:
On the injective norm and characterization of some subclasses of normal operators by inequalities or equalities
On the injective norm and characterization of some subclasses of normal operators by inequalities or equalities
Subject
:
Mthematics
Document Language
:
English
Abstract
:
Let B (H) be the C*-algebra of all bounded linear operators acting on a complex Hilbert space H. In this note, we shall show that if S is an invertible normal operator in B (H) the following estimation holds{norm of matrix} S ⊗ S-1 + S-1 ⊗ S {norm of matrix}λ ≤ {norm of matrix} S {norm of matrix} {norm of matrix} S-1 {norm of matrix} + frac(1, {norm of matrix} S {norm of matrix} {norm of matrix} S-1 {norm of matrix}) where {norm of matrix} . {norm of matrix}λ is the injective norm on the tensor product B (H) ⊗ B (H). This last inequality becomes an equality when S is invertible self-adjoint. On the other hand, we shall characterize the set of all invertible normal operators S in B (H) satisfying the relation{norm of matrix} S ⊗ S-1 + S-1 ⊗ S {norm of matrix}λ = {norm of matrix} S {norm of matrix} {norm of matrix} S-1 {norm of matrix} + frac(1, {norm of matrix} S {norm of matrix} {norm of matrix} S-1 {norm of matrix}) and also we shall give some characterizations of some subclasses of normal operators in B (H) by inequalities or equalities. © 2008 Elsevier Inc. All rights reserved.
ISSN
:
0022-247X
Journal Name
:
Journal of Mathematical Analysis and Applications
Volume
:
351
Issue Number
:
1
Publishing Year
:
2009 AH
2009 AD
Number Of Pages
:
7
Article Type
:
Article
Added Date
:
Wednesday, October 14, 2009
Researchers
Researcher Name (Arabic)
Researcher Name (English)
Researcher Type
Dr Grade
Email
عامر صديق
Ameur Seddik
Researcher
Doctorate
seddikameur@hotmail.com
Files
File Name
Type
Description
23435.pdf
pdf
Abstract
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