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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 TypeDr GradeEmail
عامر صديقAmeur SeddikResearcherDoctorateseddikameur@hotmail.com

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