Tensor Products of Locally C*-Algebras and Applications

✍ Scribed by Maria Fragoulopoulou

• Publisher: John Wiley and Sons
• Year: 1991
• Tongue: English
• Weight: 569 KB
• Volume: 153
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19911530128

✦ Synopsis

Given two lmc C*-algebras E, F denote by v, x the projective resp. injective tensorial lmc C*-topology on E 6 F [lo]. Then, E 5 x 5 v 5 a, where E, a the projective resp. biprojective tensorial topology on E 8 F. If now, F is commutative and A ( F ) denotes the GEL'FAND space of F, one obtains under suitable conditions on F that E 6% F is realized by the locally C*-algebra C c ( A ( F ) , E ) of all E-valued continuous maps on %(F) with the topology "c" of compact convergence (Theorem 2.6). Thus, one obtains sufficient conditions under which E = x on E €3 F (Theorem 2.7). Furthermore, sufficient conditions are presented under which v becomes greater than certain other tensorial lmc C*-topologies (Theorems 2.7,2.8). On the other hand, Corollary 2.4, gives conditions for the existence of continuous faithful *-representations on an lmc C*-algebra, which is the case for some of the previous results. Based on Section 2, Section 3 presents interesting applications in the representation theory of tensor product lmc *-algebras.