Extended spectrum, extended eigenspaces and normal operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:418

Article

Cassier, Gilles¹  Alkanjo, Hasan¹ 

[1] Univ Lyon 1, Inst Camille Jordan, CNRS UMR 5208, F-69622 Villeurbanne, France

关键词: Extended eigenvalues;    Extended eigenspaces;    Normal operators;    Product of a positive operator by a self-adjoint one;   

DOI  :  10.1016/j.jmaa.2014.03.062

来源: Elsevier

【 摘 要 】

We say that a complex number lambda is an extended eigenvalue of a bounded linear operator T on a Hilbert space H if there exists a nonzero bounded linear operator X acting on H, called extended eigenvector associated to lambda, and satisfying the equation TX = lambda XT. In this paper we describe the sets of extended eigenvalues and extended eigenvectors for the product of a positive and a self-adjoint operator which are both injective. We also treat the case of normal operators. (C) 2014 Published by Elsevier Inc.

【 授权许可】

Free