an:06587849
Zbl 1361.46004
Bartsch, Ren??; Poppe, Harry
An abstract algebraic-topological approach to the notions of a first and second dual space. III
EN
N. Z. J. Math. 46, 1-8 (2016).
00355827
2016
j
46A20 46B10 46H15 46L05 46L10
second dual; noncommutative \(C^{*}\)-algebra; Gelfand theorem
Summary: 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 prequel, 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, whose analogues are known in the commutative setting.
For Part I see [Theory and applications of proximity, nearness and uniformity. Caserta: Dipartimento di Matematica, Seconda Universit?? di Napoli; Rome: Aracne. 275--297 (2009; Zbl 1235.46007)], for Part II see [Int. J. Pure Appl. Math. 84, No. 5, 651--667 (2013)].
Zbl 1235.46007