Contractible quantum Arens–Michael algebras

Volume 91 / 2010

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


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.


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

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