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Complete orthogonal decomposition homomorphisms between matrix ordered Hilbert spaces
Authors:Yasuhide Miura  Kiminao Nishiyama
Institution:Department of Mathematics, Faculty of Humanities and Social Sciences, Iwate University, Morioka, 020-8550, Japan ; Niitsu Senior High School, Niitsu, 956-0832, Japan
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.

Keywords:Standard form of von Neumann algebra  completely positive map  matrix ordered Hilbert space  orthogonal decomposition homomorphism
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