Multidimensional operator multipliers

K. Juschenko, Ivan Todorov, L. Turowska

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

We introduce multidimensional Schur multipliers and characterise them, generalising well-known results by Grothendieck and Peller. We define a multidimensional version of the two-dimensional operator multipliers studied recently by Kissin and Shulman. The multidimensional operator multipliers are defined as elements of the minimal tensor product of several C *-algebras satisfying certain boundedness conditions. In the case of commutative C*-algebras, the multidimensional operator multipliersreduce to continuousmul-tidimensional Schur multipliers. We show that the multiplierswith respect to some given representations of the corresponding C*-algebrasdo not change if the representations are replaced by approximately equivalent ones. We establish a non-commutative and multidimensional version of the characterisations by Grothendieck and Peller which shows that universal operator multipliers can be obtained ascertain weak limits of elements of the algebraic tensor product of the corresponding C *-algebras.
Original languageEnglish
Pages (from-to)4683-4720
Number of pages38
JournalTransactions of the American Mathematical Society
Volume361
Issue number9
DOIs
Publication statusPublished - Sep 2009

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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