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Closed operators affiliated with a Banach algebra of operators

100%

Barnes B. A.

Studia Mathematica

1991-1992

tom 101

nr 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.

Perturbation theory relative to a Banach algebra of operators

100%

Barnes B. A.

Studia Mathematica

1993

tom 106

nr 2

153-174

Let ℬ be a Banach algebra of bounded linear operators on a Banach space X. Let S be a closed linear operator in X, and let R be a linear operator in X. In this paper the spectral and Fredholm theory relative to ℬ of the perturbed operator S + R is developed. In particular, the situation where R is S-inessential relative to ℬ is studied. Several examples are given to illustrate the usefulness of these concepts.

Ograniczanie wyników

2 Studia Mathematica

2 Barnes B. A.

1 1993

1 1992

Wyniki wyszukiwania

Closed operators affiliated with a Banach algebra of operators

Perturbation theory relative to a Banach algebra of operators