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Maximality properties for isometric interpolating sequences and sequences of trivial points in the spectrum of H∞

✍ Scribed by Raymond Mortini

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
226 KB
Volume
278
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Let (x~n~) be an isometric interpolating sequence or a sequence of trivial points in the spectrum of H^∞^. It is shown that either every cluster point of that sequence has a maximal support set or there exists y ∈ M(H^∞^+C) such that the support of x~n~ is contained in the support of y for infinitely many n. Similar results for Gleason parts are obtained, too. We also investigate the H^∞^‐convex hulls of countable unions of support sets and show that whenever supp x ⊂ supp y and x /∈ $ \overline {P(y)} $, then the H^∞^‐convex hull of supp x does not meet $ \overline {P(y)} $. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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