Search results for "Partial algebras of operators"
showing 2 items of 2 documents
CQ *-algebras of measurable operators
2022
Abstract We study, from a quite general point of view, a CQ*-algebra (X, đť–€0) possessing a sufficient family of bounded positive tracial sesquilinear forms. Non-commutative L 2-spaces are shown to constitute examples of a class of CQ*-algebras and any abstract CQ*-algebra (X, đť–€0) possessing a sufficient family of bounded positive tracial sesquilinear forms can be represented as a direct sum of non-commutative L 2-spaces.
Quasi *-algebras of measurable operators
2009
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 {\em sufficient} family of bounded positive sesquilinear forms satisfying 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 $(\X,\Ao)$ possessing a sufficient family of bounded positive tracial sesquilinear forms can be represented as a CQ*-algebra of this type.