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 Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2014, Issue 10(121), Pages 55–67 (Mi vsgu449)

Mathematics

Metric and topological freedom for sequential operator spaces

N. T. Nemesh, S. M. Shteiner

Moscow State University, 119991, Russian Federation

Abstract: In 2002 Anselm Lambert in his PhD thesis [1] introduced the definition of sequential operator space and managed to establish a considerable amount of analogs of corresponding results in operator space theory. Informally speaking, the category of sequential operator spaces is situated ”between” the categories of normed and operator spaces. This article aims to describe free and cofree objects for different versions of sequential operator space homology. First of all, we will show that duality theory in above-mentioned category is in many respects analogous to that in the category of normed spaces. Then, based on those results, we will give a full characterization of both metric and topological free and cofree objects.

Keywords: sequential operator space, sequentially bounded operator, duality, framed category, admissible epimorphism, admissible monomorphism, freedom, cofreedom.

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Document Type: Article
UDC: 517.986.22

Citation: N. T. Nemesh, S. M. Shteiner, “Metric and topological freedom for sequential operator spaces”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2014, no. 10(121), 55–67

Citation in format AMSBIB
\Bibitem{NemSht14} \by N.~T.~Nemesh, S.~M.~Shteiner \paper Metric and topological freedom for sequential operator spaces \jour Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya \yr 2014 \issue 10(121) \pages 55--67 \mathnet{http://mi.mathnet.ru/vsgu449}