Geodesic
Closed operators affiliated with a Banach algebra of operators
Studia Mathematica, Tome 101 (1991) no. 3, pp. 215-240

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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.
DOI : 10.4064/sm-101-3-215-240
Keywords: closed operator, spectrum, Fredholm operator, semigroup of operators, Banach algebra

Bruce A. Barnes 1

1 
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Bruce A. Barnes. Closed operators affiliated with a Banach algebra of operators. Studia Mathematica, Tome 101 (1991) no. 3, pp. 215-240. doi: 10.4064/sm-101-3-215-240

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