Bounded elements in certain topological partial $^*$-algebras
Volume 203 / 2011
Studia Mathematica 203 (2011), 223-251
MSC: Primary 47L60; Secondary 46H15.
DOI: 10.4064/sm203-3-2
Abstract
We continue our study of topological partial $^*$-algebras, focusing on the interplay between various partial multiplications. The special case of partial $^*$-algebras of operators is examined first, in particular the link between strong and 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 $\cal M$-bounded. Finally, some remarks are made concerning representations in terms of so-called partial $GC^*$-algebras of operators.
