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'Orléans, Département de Mathématiques, B.P. 6759, 45067 Orléans Cedex 2, FRANCE
(2) Université d'Orléans, 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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