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Maximality properties for isometric interpolating sequences and sequences of trivial points in the spectrum of H ∞
Author(s) -
Mortini Raymond
Publication year - 2005
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310259
Subject(s) - mathematics , convex hull , combinatorics , sequence (biology) , countable set , spectrum (functional analysis) , isometric exercise , regular polygon , point (geometry) , set (abstract data type) , hull , geometry , medicine , genetics , marine engineering , engineering , physics , quantum mechanics , computer science , biology , programming language , physical therapy
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)