Closed operators affiliated with a Banach algebra of operators

Volume 101 / 1992

Bruce A. Barnes Studia Mathematica 101 (1992), 215-240 DOI: 10.4064/sm-101-3-215-240


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.


  • Bruce A. Barnes

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