Closed Range Property for Holomorphic Semi-Fredholm Functions

Abstract

Given Banach spaces X and Y , we show that, for each operator-valued analytic map α ∈ O(D, L(Y, X)) satisfying the finite-As an application we deduce that the generalized range R ∞ (T ) = k≥1 |α|=k T α X of a commuting multioperator T ∈ L(X) n with dim(X/ n i=1 TiX) < ∞ can be represented as a suitable spectral subspace. Mathematics Subject Classification (2000). Primary 47A13, 32C35; Secondary 47A11, 47A53.