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For a class of essentially normal operators, we characterize their norm closures of (U+K)-orbits. Moreover, we introduce a notion of the quasiapproximate (U+K)-equivalence of essentially normal operators and determine completely the quasiapproximate (U+K)-invariants. Finally, we give the canonical forms of essentially normal operators under this quasiap-proximate (U+K)-equivalence.

Essentially normal,， Bergmann operator,， Cowen-Douglas operator,， Unilateral weghted shift,， Quasiapproximate (， U+， K)， -equivalence.，

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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).

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吉林大学，吉林

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