We consider quantum analogues of locally convex spaces in terms of the non-coordinate approach. We introduce the notions of a quantum Arens-Michael algebra and a quantum polynormed module, and also quantum versions of projectivity and contractibility. We prove that a quantum Arens-Michael algebra is contractible if and only if it is completely isomorphic to a Cartesian product of full matrix C*-algebras. Similar results in the framework of traditional (non-quantum) approach are established, at the moment, only under some additional assumptions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc91-0-25,
author = {Nina V. Volosova},
title = {Contractible quantum Arens-Michael algebras},
journal = {Banach Center Publications},
volume = {89},
year = {2010},
pages = {423-440},
zbl = {1217.46037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc91-0-25}
}
Nina V. Volosova. Contractible quantum Arens-Michael algebras. Banach Center Publications, Tome 89 (2010) pp. 423-440. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc91-0-25/