NORM-CLOSED BIMODULES OF NEST ALGEBRAS

NORM-CLOSED BIMODULES OF NEST ALGEBRAS

We study the support and essential support functions of a norm-closed bimodule of a nest algebra. An allowable support function pair determines a maximal bimodule. There is also a natural candidate for the minimal bimodule for a given support function pair. We determine precisely when this candidate...

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Veröffentlicht in:Journal of operator theory 1998-01, Vol.39 (1), p.59-87
Hauptverfasser: DAVIDSON, KENNETH R., DONSIG, ALLAN P., HUDSON, TIMOTHY D.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Atoms
Decreasing sequences
Finite sums
Increasing sequences
Mathematical theorems
Mathematical vectors
Unit vectors
Urelements
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Zusammenfassung:We study the support and essential support functions of a norm-closed bimodule of a nest algebra. An allowable support function pair determines a maximal bimodule. There is also a natural candidate for the minimal bimodule for a given support function pair. We determine precisely when this candidate is the minimal element. In the other cases, this module is still the intersection of all bimodules with a given support function pair, but it is not in this class itself.
ISSN:0379-4024
1841-7744