Moving Weyl's Theorem from f (T ) to T

M. Febronio Rodríguez, BUAP, Facultad de Ciencias Fı́sico-Matemáticas, B.P. Duggal, S.V Djordjević, BUAP, Facultad de Ciencias Fı́sico-Matemáticas
2017 Extracta Mathematicae  
Schmoeger has shown that if Weyl's theorem holds for an isoloid Banach space operator T ∈ B(X) with stable index, then it holds for f (T ) whenever f ∈ Holo σ(T ) is a function holomorphic on some neighbourhood of the spectrum of T . In this note we establish a converse.
doi:10.17398/2605-5686.33.2.208 fatcat:iigsgqbt4bgono3xdcc67msa6i