A note on injective envelopes and von Neumann algebras

Abstract

The article exhibits certain relations between the injective envelope I(A) of a C*-algebra A and the von Neumann algebra generated by a representation lambda of A provided it is injective. More specifically we show that there exist positive retractions sigma : /lambda (A)'' ---> I(A) which are close to being *-homomorphisms in the sense that they are Jordan homomorphisms of the underlying Jordan algebras, and the kernel of /sigma is given by a twosided ideal.

arXiv commentThe proof of the main result contains some grave errors. The article has been overworked, replaced and extended by the recently submitted article "The Jordan lattice completion and a note on injective envelopes and von Neumann algebras" (arXiv:1804.05701) where the main result of the former paper is contained in a slightly modified version with an altogether different proof