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2005年11月15日

【期刊论文】QUASITRIANGULAR + SMALL COMPACT=STRONGLY IRREDUCIBLE

纪友清， YOU QING JI

TRANSACTIONS OF THE AMERICAN MATHEMATICAI, SOCIETY Volume 351, Nomber 11, Pages 4657-4673，-0001，（）：

-1年11月30日

摘要

Let T be a bounded linear operator acting on a separable infinite dimensional Hilbert space. Let E be a positive number. In this article, we prove that the perturbation of T by a compact operator K with ‖K‖<E can be strongly irreducible if T is a quasitriangular operator with the spectrum σ(T) connected. The Main Theorem of this article nearly answers the question below posed by D. A. Herrero. Suppose that T is a bounded linear operator acting on a separable infinite dimensional Hilbert space with σ(T) connected. Let ε>0 be given. Is there a compact operator K with ‖K‖<ε such that T+K is strongly irreducible?

Weyl spectrum,， index,， strongly irreducible,， quasituiangular.，

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2005年11月15日

【期刊论文】HE STRONGLY IRREDUCIBLE OPERATORS IN NEST ALGEBRAS1

纪友清， You Qing， Ji， Chun Lan Jiang， and Zong Yao Wang

Integr. equ. oper. theory 28(1997)28-44，-0001，（）：

-1年11月30日

摘要

An operator T on H is called strongly irreducible if T does not commute with any nontrivial idernpotent operator In this paper, we first show that each nest algebra T(N) has strong y rreducible operators, Secondly. we obtain a characterization of operators which can be uniquely written as a direct sum of finitely many strongly irreducible operators. Finafiy, we characterize the strongly irreducibility of operators in a nest algebra T(N).