Some seminorms on quasi $^*$-algebras
Volume 158 / 2003
Studia Mathematica 158 (2003), 99-115
MSC: Primary 46K05.
DOI: 10.4064/sm158-2-1
Abstract
Different types of seminorms on a quasi $^*$-algebra $({{{\mathfrak A}}},{{{\mathfrak A}}}_0)$ are constructed from a suitable family ${\mathcal F}$ of sesquilinear forms on ${{{\mathfrak A}}}$. Two particular classes, extended $C^*$-seminorms and $CQ^*$-seminorms, are studied in some detail. A necessary and sufficient condition for the admissibility of a sesquilinear form in terms of extended $C^*$-seminorms on $({{{\mathfrak A}}},{{{\mathfrak A}}}_0)$ is given.
