Ranges of bimodule projections and reflexivity

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4 Citations (Scopus)

Abstract

We develop a general framework for reflexivity in dual Banach
spaces, motivated by the question of when the weak* closed linear
span of two reflexive masa-bimodules is automatically reflexive. We
establish an affirmative answer to this question in a number of
cases by examining two new classes of masa-bimodules, defined in
terms of ranges of masa-bimodule projections. We give a number of
corollaries of our results concerning operator and spectral
synthesis, and show that the classes of masa-bimodules we study are
operator synthetic if and only if they are strong operator Ditkin.
Original languageEnglish
Pages (from-to)4891-4915
Number of pages25
JournalJournal of Functional Analysis
Volume262
Issue number11
Publication statusPublished - 01 Jun 2012

Keywords

  • Schur idempotents, masa-bimodules, projections, reflexivity

ASJC Scopus subject areas

  • Analysis

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