DC MetaData for: Applications of the Bartsch-Poppe duality approach

Harry Poppe

Applications of the Bartsch-Poppe duality approach

The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 73, 3 - 26 (2023)

MSC:	46A20	Duality theory for topological vector spaces
	46J25	Representations of commutative topological algebras
	46L05	General theory of \(C^*\)-algebras
	46L30	States of selfadjoint operator algebras
	54C35	Function spaces in general topology
	54C45	\(C\)- and \(C^*\)-embedding

Abstract:
What is the aim of this paper?

We want to improve the definitions of the first dual space \(X^d\) and the second dual space \(X^{dd}\) of a given space, \(X\) as were defined in [1]. For this purpose we will repeat in short the very basic definitions and some results of the B/P duality approach.
We apply the B/P duality approach to get new, well arranged proofs of
- the representation of a nonunital commutative \(C^*\)-algebra (Gelfand-Naimark theorem)
- the embedding theorem of Kadison.

[1]
Bartsch, R. and Poppe, H.: An abstract algebraic-topological approach to the notions of a first and a second dual space, I. In: Theory and applications of proximity, nearness and uniformity. Caserta: Dipartimento di Matematica, Seconda Università di Napoli, Quaderni di Matematica 22; Rome: Aracne 2009, 275 - 297

karin.martin@uni-rostock.de
Seite generiert am 22.11.2023