# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Quasi *-algebras of measurable operators

### Tom 172 / 2006

Studia Mathematica 172 (2006), 289-305 MSC: Primary 46L08; Secondary 46L51, 47L60. DOI: 10.4064/sm172-3-6

#### Streszczenie

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.

#### Autorzy

• Fabio BagarelloDipartimento di Metodi e Modelli Matematici
Università di Palermo
I-90128 Palermo, Italy
e-mail
• Camillo TrapaniDipartimento di Matematica ed Applicazioni
Università di Palermo
I-90123 Palermo, Italy
e-mail
• Salvatore TrioloDipartimento di Matematica ed Applicazioni
Università di Palermo
I-90123 Palermo, Italy
e-mail

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