Closed operators affiliated with a Banach algebra of operators
Volume 101 / 1992
Studia Mathematica 101 (1992), 215-240
DOI: 10.4064/sm-101-3-215-240
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.
