Schur and operator multipliers

Volume 91 / 2010

Ivan G. Todorov, Lyudmila Turowska Banach Center Publications 91 (2010), 385-410 MSC: Primary 47L25; Secondary 46L05. DOI: 10.4064/bc91-0-23


The present article is a survey of known results on Schur and operator multipliers. It starts with the classical description of Schur multipliers due to Grothendieck, followed by a discussion of measurable Schur multipliers and a generalisation of Grothendieck's Theorem due to Peller. Thereafter, a non-commutative version of Schur multipliers, called operator multipliers and introduced by Kissin and Schulman, is discussed, and a characterisation extending the description in the commutative case is presented. Finally, multidimensional versions of Schur and operator multipliers are considered. The article contains a brief discussion of some applications of Schur multipliers, including double operator integrals and multipliers of group algebras.


  • Ivan G. TodorovDepartment of Pure Mathematics
    Queen's University Belfast
    Belfast BT7 1NN, United Kingdom
  • Lyudmila TurowskaDepartment of Mathematical Sciences
    Chalmers University of Technology and University of Gothenburg
    Gothenburg SE-412 96, Sweden

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