Multidimensional operator multipliers

K. Juschenko*, I. G. Todorov, L. Turowska

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


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 (US)
Pages (from-to)4683-4720
Number of pages38
JournalTransactions of the American Mathematical Society
Issue number9
StatePublished - Sep 2009


  • C-algebra
  • Multidimensional
  • Multiplier

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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