1Dipartimento di Metodi e Modelli Matematici Università di Palermo I-90128 Palermo, Italy 2Dipartimento di Matematica ed Applicazioni Università di Palermo I-90123 Palermo, Italy
Studia Mathematica, Tome 172 (2006) no. 3, pp. 289-305
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.
Keywords:
non commutative p spaces shown constitute examples class banach quasi * algebras called * algebras geq proved possess sufficient family bounded positive sesquilinear forms certain invariance properties * algebras measurable operators finite von neumann algebra constructed proven abstract * algebra mathfrak cal sufficient family bounded positive tracial sesquilinear forms represented * algebra type
1
Dipartimento di Metodi e Modelli Matematici Università di Palermo I-90128 Palermo, Italy
2
Dipartimento di Matematica ed Applicazioni Università di Palermo I-90123 Palermo, Italy
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author = {Fabio Bagarello and Camillo Trapani and Salvatore Triolo},
title = {Quasi *-algebras of measurable operators},
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Fabio Bagarello; Camillo Trapani; Salvatore Triolo. Quasi *-algebras of measurable operators. Studia Mathematica, Tome 172 (2006) no. 3, pp. 289-305. doi: 10.4064/sm172-3-6
