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Page's theorem for ordered groups
by
Mihaly Bakonyi
Georgia State University
Let G be a compact abelian group having the property that its character group \Gamma is ordered by a semigroup P. We prove that every operator-valued function k on G of the form k(x)=\sum\gamma in (-P)\gamma(x)k\gamma, such that the Hankel operator Hk is bounded, has an essentially bounded extension K with ||K||\infty=||Hk||. The proof is based on Arveson's Extension Theorem for completely positive functions on C*-algebras. Among the corollaries we have a Carathéodory-Fejér type result for analytic operator-valued functions defined on such groups.
Date received: June 14, 2002
Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caiz-68.