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.
Cite
@article{arxiv.1310.3636,
title = {A note on injective envelopes and von Neumann algebras},
author = {Ulrich Haag},
journal= {arXiv preprint arXiv:1310.3636},
year = {2024}
}
Comments
The 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