The Schur product is the commutative operation of entrywise multiplication of two (possibly infinite) matrices. If we fix a matrix A and require that the Schur product of A with the matrix of any bounded operator is again the matrix of a bounded operator, then A is said to be a Schur multiplier; Schur multiplication by A then turns out to be a completely bounded map. The Schur multipliers were characterised by Grothendieck in the 1950s. In a 2006 paper, Kissin and Shulman study a noncommutative generalisation which they call "operator multipliers", in which the theory of operator spaces plays an important role. We will present joint work with Katja Juschenko, Ivan Todorov and Ludmilla Turowska in which we determine the operator multipliers which are completely compact (that is, they satisfy a strengthening of the usual notion of compactness which is appropriate for completely bounded maps).
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Last updated 18 April 2008. This page was created and is maintained by Stephen Wills (s.wills@ucc.ie).