An operator corona theorem for a class of subspaces of H∞

Abstract

Let E;E be separable Hilbert spaces. If S is an open subset of T, then AS(L(E;E)) denotes the space of all functions f : D [ S ! L(E;E) that are holomorphic in D, and bounded and continuous on D [ S. In this article we prove the following main results: 1. A theorem concerning the approximation of f 2 AS(L(E;E)) by a function F that is holomorphic in a neighbourhood of D[S and such that the error