Perturbation theory relative to a Banach algebra of operators
Tom 106 / 1993
Studia Mathematica 106 (1993), 153-174
DOI: 10.4064/sm-106-2-153-174
Streszczenie
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.
