Compact operators without extended eigenvalues

被引：16
作者：
Shkarin, S. [1 ]
机构：
[1] Kings Coll London, Dept Math, London WC2R 2LS, England
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2007年 / 332卷 / 01期
关键词：
extended eigenvalues; compact operators; quasinilpotent operators; similarity;
D O I：
10.1016/j.jmaa.2006.10.035
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A complex number lambda is called an extended eigenvalue of a bounded linear operator T on a Banach space B if there exists a non-zero bounded linear operator X acting on B such that XT = lambda TX. We show that there are compact quasinilpotent operators on a separable Hilbert space, for which the set of extended eigenvalues is the one-point set {1}. (c) 2006 Elsevier Inc. All rights reserved.
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页码：455 / 462
页数：8
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