# Wydawnictwa / Banach Center Publications / Wszystkie tomy

## Contractible quantum Arens–Michael algebras

### Tom 91 / 2010

Banach Center Publications 91 (2010), 423-440 MSC: Primary 46L07, 46H20, 46M20; Secondary 46H25. DOI: 10.4064/bc91-0-25

#### Streszczenie

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 $C^{\ast}$-algebras. Similar results in the framework of traditional (non-quantum) approach are established, at the moment, only under some additional assumptions.

#### Autorzy

• Nina V. VolosovaFaculty of Mechanics and Mathematics
Lomonosov Moscow State University
Moscow 119991, Russia
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