Bounded elements in certain topological partial *-algebras

Details Bounded elements in certain topological partial *-algebras Bounded elements in certain topological partial *-algebras

2012-03-02

arxiv.org/abs/1203.0515v1

Studia Mathematica 203 (2011) 223-251

Mathematics

Rings and Algebras

32 pages

Scientific paper

We continue our study of topological partial *algebras, focusing our attention to the interplay between the various partial multiplications. The special case of partial *-algebras of operators is examined first, in particular the link between the strong and the weak multiplications, on one hand, and invariant positive sesquilinear (ips) forms, on the other. Then the analysis is extended to abstract topological partial *algebras, emphasizing the crucial role played by appropriate bounded elements, called $\M$-bounded. Finally, some remarks are made concerning representations in terms of the so-called partial GC*-algebras of operators.

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