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arXiv · 1310.3636

A note on injective envelopes and von Neumann algebras

Ulrich Haag
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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.

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Ulrich Haag. 2013-10-14. A note on injective envelopes and von Neumann algebras. https://arxiv.org/abs/1310.3636

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