Multidimensional operator multipliers
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- by K. Juschenko, I. G. Todorov and L. Turowska PDF
- Trans. Amer. Math. Soc. 361 (2009), 4683-4720 Request permission
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 multipliers reduce to continuous multidimensional Schur multipliers. We show that the multipliers with respect to some given representations of the corresponding $C^*$-algebras do 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 as certain weak limits of elements of the algebraic tensor product of the corresponding $C^*$-algebras.References
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Additional Information
- K. Juschenko
- Affiliation: Department of Mathematics, Chalmers Institute of Technology and University of Gothenburg, SE-412 96 Gothenburg, Sweden
- Email: jushenko@chalmers.se
- I. G. Todorov
- Affiliation: Department of Pure Mathematics, Queen’s University Belfast, Belfast BT7 1NN, United Kingdom
- MR Author ID: 693462
- Email: i.todorov@qub.ac.uk
- L. Turowska
- Affiliation: Department of Mathematics, Chalmers Institute of Technology and University of Gothenburg, SE-412 96 Gothenburg, Sweden
- Email: turowska@chalmers.se
- Received by editor(s): July 5, 2007
- Published electronically: April 10, 2009
- © Copyright 2009 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 361 (2009), 4683-4720
- MSC (2000): Primary 46L07; Secondary 47L25
- DOI: https://doi.org/10.1090/S0002-9947-09-04771-0
- MathSciNet review: 2506424