On the injective norm and characterization of some subclasses of normal operators by inequalities or equalities

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:351

Article

Seddik, Ameur

关键词: Tensor product space;    Injective norm;    Self-adjoint operator;    Unitary operator;    Normal operator;   

DOI  :  10.1016/j.jmaa.2008.10.008

来源: Elsevier

【 摘 要 】

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 parallel to S circle times S(-1) + S(-1) circle times S parallel to(lambda) <= parallel to S parallel to parallel to S(-1)parallel to + 1/parallel to S parallel to parallel to S(-1)parallel to where parallel to.parallel to(lambda) is the injective norm on the tensor ptoduct B(H) circle times 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 parallel to S circle times S(-1) + S(-1) circle times S parallel to(lambda) = parallel to S parallel to parallel to S(-1)parallel to + 1/parallel to S parallel to parallel to S(-1)parallel to and also we shall give some characterizations of some subclasses of normal operators in B(H) by inequalities or equalities. (c) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

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