Strong Morita equivalence for conditional expectations
Abstract
We consider two inclusions of -algebras whose small -algebras have approximate units of the large -algebras and their two spaces of all bounded bimodule linear maps. We suppose that the two inclusions of -algebras are strongly Morita equivalent. In this paper, we shall show that there exists an isometric isomorphism from one of the spaces of all bounded bimodule linear maps to the other space and we shall study on basic properties about the isometric isomorphism. And, using this isometric isomorphism, we define the Picard group for a bimodule linear map and discuss on the Picard group for a bimodule linear map.
Keywords
Cite
@article{arxiv.2009.08252,
title = {Strong Morita equivalence for conditional expectations},
author = {Kazunori Kodaka},
journal= {arXiv preprint arXiv:2009.08252},
year = {2021}
}
Comments
23 pages. The title is changed. This is a revised version of arXiv:2009.08252 and arXiv:2001.10136. This article is rewritten combining arXiv:2009.08252 and arXiv:2001.10136