Journal of Operator Theory

Volume 48, Issue 3, Supplementary 2002 pp. 549-571.

Haagerup approximation property for finite von Neumann algebras

Authors: Paul Jolissaint
Author institution: Institut de Mathemathiques, Universite de Neuchatel, Emile-Argand 11, CH-2000 Neuchatel, Switzerland

Summary: We study finite von Neumann algebras $M$ that admit an approximate identity made with completely positive normal maps whose extention to $L^2(M)$ are compact operators. We prove heredity results, and we state sufficient conditions on actions of countable groups to ensure that the crossed product algebras have the same property.

Keywords: von Neumann algebras, completely positive maps, Haagerup property, crossed products

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