Authors

D. Han; D. Larson; Z. Pan;W. Wogen

Comments

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Abbreviated Journal Title

Indiana Univ. Math. J.

Keywords

triangular operators; extension of operators; extension spectrum; spectral mapping theorem; Kato spectrum; REFLEXIVITY; Mathematics

Abstract

We introduce the concept of the extension spectrum of a Hilbert space operator. This is a natural subset of the spectrum which plays an essential role in dealing with certain extension properties of operators. We prove that it has spectral-like properties and satisfies a holomorphic version of the Spectral Mapping Theorem. We establish structural theorems for algebraic extensions of triangular operators which use the extension spectrum in a natural way. The extension spectrum has some properties in common with the Kato spectrum, and in the final section we show how they are different and we examine their inclusion relationships.

Journal Title

Indiana University Mathematics Journal

Volume

53

Issue/Number

4

Publication Date

1-1-2004

Document Type

Article

Language

English

First Page

1151

Last Page

1169

WOS Identifier

WOS:000224787900010

ISSN

0022-2518

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