# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Bounded elements and spectrum in Banach quasi $^*$-algebras

### Tom 172 / 2006

Studia Mathematica 172 (2006), 249-273 MSC: Primary 46L08; Secondary 46L51, 47L60. DOI: 10.4064/sm172-3-4

#### Streszczenie

A normal Banach quasi $^*$-algebra $({\mathfrak X},)$ has a distinguished Banach $^*$-algebra ${\mathfrak X}_{\rm b}$ consisting of {bounded} elements of ${\mathfrak X}$. The latter $^*$-algebra is shown to coincide with the set of elements of ${\mathfrak X}$ having finite spectral radius. If the family ${\cal P}({\mathfrak X})$ of bounded invariant positive sesquilinear forms on ${\mathfrak X}$ contains sufficiently many elements then the Banach $^*$-algebra of bounded elements can be characterized via a $C^*$-seminorm defined by the elements of ${\cal P}({\mathfrak X})$.

#### Autorzy

• Camillo TrapaniDipartimento di Matematica ed Applicazioni
Università di Palermo
I-90123 Palermo, Italy
e-mail

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