Search results for " 47L60"
showing 3 items of 3 documents
Bounded elements in certain topological partial *-algebras
2011
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.
Locally convex quasi C*-algebras and noncommutative integration
2015
In this paper we continue the analysis undertaken in a series of previous papers on structures arising as completions of C*-algebras under topologies coarser that their norm and we focus our attention on the so-called {\em locally convex quasi C*-algebras}. We show, in particular, that any strongly *-semisimple locally convex quasi C*-algebra $(\X,\Ao)$, can be represented in a class of noncommutative local $L^2$-spaces.
Fully representable and*-semisimple topological partial*-algebras
2012
We continue our study of topological partial *-algebras, focusing our attention to *-semisimple partial *-algebras, that is, those that possess a {multiplication core} and sufficiently many *-representations. We discuss the respective roles of invariant positive sesquilinear (ips) forms and representable continuous linear functionals and focus on the case where the two notions are completely interchangeable (fully representable partial *-algebras) with the scope of characterizing a *-semisimple partial *-algebra. Finally we describe various notions of bounded elements in such a partial *-algebra, in particular, those defined in terms of a positive cone (order bounded elements). The outcome …