Vol. 120, No. 1, 1985

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P. Ghez, R. Lima and J. E. Roberts

Vol. 120 (1985), No. 1, 79–109

A W-category is the categorical counterpart of a von Neumann algebra with an abstract definition equivalent to a concrete definition in terms of operators between Hilbert spaces. We develop the elementary theory of W-categories including modular theory and the comparison theory of objects (equivalence and quasiequivalence). We also characterize certain W-categories in terms of the W-category of projections in a von Neumann algebra, self-dual Hermitian modules for a von Neumann algebra or normal representations of a von Neumann algebra. This leads naturally to a discussion of the Morita equivalence of von Neumann algebras and of W-categories.

Mathematical Subject Classification 2000
Primary: 46L10
Secondary: 46L05, 46M15
Received: 2 February 1984
Revised: 4 April 1984
Published: 1 November 1985
P. Ghez
R. Lima
J. E. Roberts