Complete orthogonal decomposition homomorphisms between matrix ordered Hilbert spaces

Miura, Yasuhide; Nishiyama, Kiminao

doi:10.1090/S0002-9939-00-05745-2

Complete orthogonal decomposition homomorphisms between matrix ordered Hilbert spaces
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by Yasuhide Miura and Kiminao Nishiyama PDF

Proc. Amer. Math. Soc. 129 (2001), 1137-1141 Request permission

Abstract:

The purpose of this paper is to show that a complete order homomorphism and a complete orthogonal decomposition homomorphism between the non-commutative $L^{2}$-spaces induce respectively an isomorphism and a $*$-isomorphism between the associated reduced von Neumann algebras.

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