Quasi *-algebras of measurable operators
Volume 172 / 2006
Studia Mathematica 172 (2006), 289-305
MSC: Primary 46L08; Secondary 46L51, 47L60.
DOI: 10.4064/sm172-3-6
Abstract
Non-commutative $L^p$-spaces are shown to constitute examples of a class of Banach quasi $^*$-algebras called $CQ^*$-algebras. For $p\geq 2$ they are also proved to possess a sufficient family of bounded positive sesquilinear forms with certain invariance properties. $CQ^*$-algebras of measurable operators over a finite von Neumann algebra are also constructed and it is proven that any abstract $CQ^*$-algebra $(\mathfrak X,{\cal A}_0)$ with a sufficient family of bounded positive tracial sesquilinear forms can be represented as a $CQ^*$-algebra of this type.
