| Abstract: | We extend results in [CS] to the multilinear setting, defining the n-fold central Haagerup tensor product of a von Neumann algebra R and showing that the natural map from this space into the multilinear completely bounded operators on R is an isometry. We develop the notion of an elementary operator R on a C*-algebra A which leaves invariant a subalgebra C of A. We show that such an operator cannot always be written as a finite sum of length one operators which leave C invariant. We define the normalizer S[N] of a nest algebra A[N] and develop a characterization of elements of S[N] in terms of certain endomorphisms on N when N is continuous. This leads to some structural results for S[N]. |
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