Components of generalized Kato resolvent set and single-valued extension property

Abstract

In this paper, we use the constancy of certain subspace valued mappings on the components of the generalized Kato resolvent set and the equivalences of the single-valued extension property at a point 0 for operators which admit a generalized Kato decomposition to obtain a classification of the components of the generalized Kato resolvent set of operators. We also give some applications of these results.

Keywords

Banach space / generalized Kato decomposition / single-valued extension property

References

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