Journal of Operator Theory

Volume 32, Issue 1, Summer 1994 pp. 111-156.

Correspondances d’indice fini I: Indice d’un vecteur

Authors: Yves Denizeau (1) and Jean-François Havet (2)
Author institution:(1) Université d’Orleans, Département de Mathématiques, B.P. 6759, 45067 Orléans Cedex 2, FRANCE
(2) Université d’Orleans, Département de Mathématiques, B.P. 6759, 45067 Orléans Cedex 2, FRANCE

Summary: Let M, N be von Neumann algebras, X an M-N-correspondence and Y an N-M-correspondence. We introduce and characterize Hilbert-Schmidt operators between Y and X. These operators are our main tool to define the index of a vector in the composition Y \otimes X. In a subsequent paper, this notion will be used to study the dimension of a correspondence.

Keywords: Index, correspondence.

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