Completely isometric representations of McbA(G) and UCB(Ĝ)ß

Matthias Neufang, Zhong-Jin Ruan, Nico Spronk

Research output: Contribution to journalArticlepeer-review

Abstract

Let G be a locally compact group. It is shown that there exists a natural completely isometric representation of the completely bounded Fourier multiplier algebra McbA(G), which is dual to the representation of the measure algebra M(G), on B(L2(G)). The image algebras of M(G) and M cbA(G) in CBσ(B(L2(G))) are intrinsically characterized, and some commutant theorems are proved. It is also shown that for any amenable group G, there is a natural completely isometric representation of UCB(Ĝ)ß on B(L2(G)), which can be regarded as a duality result of Neufang's completely isometric representation theorem for LUC(G)ß.

Original languageEnglish (US)
Pages (from-to)1133-1161
Number of pages29
JournalTransactions of the American Mathematical Society
Volume360
Issue number3
DOIs
StatePublished - Mar 2008

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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