An Abstract Algebraic-Topological Approach to the Notions of a First and Second Dual Space III


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New Zealand Journal of Mathematics

Vol. 46, (2016), Pages 1-8

René Bartsch

TU Darmstadt,

Dept. of Math.,

Schlossgartenstr. 7,

64289 Darmstadt,


Harry Poppe

University of Rostock,

Dept. of Math.,

Ulmenstr. 69,

18057 Rostock,


Abstract Here we continue to develop a concept, that generalizes the idea of the second dual space of a normed vector space in a fairly general way. As in the part before, the main tool is to recognize the "first dual" as a means to the end of the second dual. Especially, we will easily prove here some essential statements on embeddings of noncommutative C * -algebras in their second dual, as whose analogues are known in the commutative setting.

Keywords second dual, noncommutative C * -algebra, Gelfand theorem.

Classification (MSC2000) 46A20, 46B10, 46H15, 46L05, 46L10.

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