On a Localised Single–Valued Extension Property

Abstract

In this article, we investigate, a certain localised version of the single-valued extension property for a bounded linear operator on a Banach space. We show that this condition behaves canonically under the Riesz functional calculus, and derive a number of characterisations in terms of kernel-type and range-type spaces for the operator and its adjoint. The theory is exemplified in the case of isometries, analytic Toeplitz operators, invertible composition operators on Hardy spaces, and weighted shifts.