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An operator T on H is called strongly irreducible if T is not similar to any reducible operators, in this paper, we shall say 'yes' to answer the following question raised hy D. A. Herrero. G yen an operator T with connecteg spectrum a(T) and a positive number E, can we find a compact operator K with ‖K‖＜E such that T+K is strong y irreducible?

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2005年11月15日

【期刊论文】STRONGLY APPROX1MAT1VE SIMILARITY OF OPERATORS

纪友清， You Qing Ji， and Juc Xian Li

TAIWANI SE JOUKNAL OF MATJE,ATOCS Vol.5, No.4, pp. 739-753, December 2001，-0001，（）：

-1年11月30日

摘要

For the bounded linear operators acting on a complex separable Hilbert space H, we introduce a binary relation ～sas called strongly approxi-mative similarity It lies between the similarity and the essential similarity. For a class of biquasitriangular operators and a class of quasitriangular operators, this relation is characterized respectively. As a result, the relation ～sas is an equivalent relation in this two cases.

Compact operator,， spectral picture,， quasitriangular operator.，

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吉林大学，吉林

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