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ArticleOriginal scientific text

Title

Closed operators affiliated with a Banach algebra of operators

Authors 1

Affiliations

  1. Department of Mathematics, University of Oregon, Eugene, Oregon 97403, U.S.A.

Abstract

Let ℬ be a Banach algebra of bounded linear operators on a Banach space X. If S is a closed operator in X such that (λ - S)^{-1} ∈ ℬ for some number λ, then S is affiliated with ℬ. The object of this paper is to study the spectral theory and Fredholm theory relative to ℬ of an operator which is affiliated with ℬ. Also, applications are given to semigroups of operators which are contained in ℬ.

Keywords

ENG
closed operator, spectrum, Fredholm operator, semigroup of operators, Banach algebra

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Studia Mathematica
1991-1992/101/3
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Pages:
215-240
Main language of publication
English
Received
1991-08-08
Published
1992
Exact and natural sciences