Duality, Tangential Interpolation, and Toeplitz Corona Problems

Details Duality, Tangential Interpolation, and Toeplitz Corona Problems Duality, Tangential Interpolation, and Toeplitz Corona Problems

2009-12-11

arxiv.org/abs/0912.2340v2

Integral Equations Operator Theory 68 (2010), no. 3, 337-355

Mathematics

Functional Analysis

17 pages, no figures, to appear in Integral Equations and Operator Theory

Scientific paper

10.1007/s00020-010-1802-y

In this paper we extend a method of Arveson and McCullough to prove a tangential interpolation theorem for subalgebras of $H^\infty$. This tangential interpolation result implies a Toelitz corona theorem. In particular, it is shown that the set of matrix positivity conditions is indexed by cyclic subspaces, which is analogous to the results obtained for the ball and the polydisk algebra by Trent-Wick and Douglas-Sarkar.

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