Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-2006-02

March 2006

An operator corona theorem for a class of subspaces of H

Amol Sasane

Let E,F be separable Hilbert spaces and E be finite dimensional. Denote the set of all bounded linear transformations from E to F by L(E,F). Suppose that S is an open subset of the unit circle T, and let D denote the open unit disk in the complex plane. Let A(S) denote the set of all L(E,F)-valued functions f defined on the union of D and S such that f is holomorphic in D and bounded and continuous on the union of D and S. The main result in this article is that the corona theorem holds for A(S).

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