Components of generalized Kato resolvent set and single-valued extension property
The authors study the components of the generalized Kato resolvent set. From the constancy of some subspace valued mappings on the components of the generalized Kato resolvent set [\textit{W. Bouamama}, Rend. Circ. Mat. Palermo (2) 53, No.~3, 313--324 (2004; Zbl 1195.47011)] and, in the case of operators which admit a generalized Kato decomposition, the equivalences of the single-valued extension property at a point, the authors obtain a classification of these components, which extends the results of \textit{P. Aiena} and \textit{F. Villafañe} [Contemp. Math. 328, 1--14 (2003; Zbl 1057.47006)] to the components of the generalized Kato resolvent set. The authors also present some applications of their results.
scientific article; zbMATH DE number 6103003
scientific article