Quasi *-algebras of measurable operators

Details Quasi *-algebras of measurable operators Quasi *-algebras of measurable operators

2009-03-31

arxiv.org/abs/0903.5467v1

Studia Mathematica, 172, 289-305 (2006)

Physics

Mathematical Physics

Scientific paper

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.

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