×

Tensor products of enveloping locally \(C^*\)-algebras. (English) Zbl 0906.46040

Schriftenreihe des Mathematischen Instituts der Universität Münster. 3. Serie, 21. Münster: Univ. Münster, Mathematisches Institut, vi, 81 p. (1997).
This is the third booklet in the author’s series devoted to non-Banach topological *-algebras (mostly \(m\)-convex algebras called here pre Arens-Michael algebras). The first two dealt with Hilbert space representations and with symmetric algebras, the present book, however, is self-contained and can be read independently. It is devoted to enveloping algebras of a topological tensor product of two \(m\)-convex *-algebras and to the problem when an \(m\)-convex *-algebra has a \(C^*\)-enveloping algebra, i.e. an \(m\)-convex algebra with topology given by seminorms satisfying the \(C^*\) condition.
It consists of seven sections: Preliminaries, \(Q\)-algebras, *-topological tensor products, Projective and injective tensorial locally \(C^*\)-topologies, Tensor product enveloping algebras, Arens-Michael *-algebras with \(C^*\)-enveloping algebras, Appendix: a supplement to the Shirali-Ford theorem for involutive Arens-Michael algebras. Many results given here are due to the author, some of them already published, some new or improving the old ones.
The book contains many interesting examples and can be useful for graduate students or researches interested in topological algebras.

MSC:

46K05 General theory of topological algebras with involution
46H05 General theory of topological algebras
46L05 General theory of \(C^*\)-algebras
46H15 Representations of topological algebras
46M05 Tensor products in functional analysis
PDFBibTeX XMLCite