Bounded elements and spectrum in Banach quasi *-algebras

• Autorzy: Camillo Trapani
• Języki publikacji: EN

Abstrakty

EN

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

Kategorie tematyczne

• 47L60: Algebras of unbounded operators; partial algebras of operators
• 46L08: C * -modules
• 46L51: Noncommutative measure and integration

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 172
• Numer: 3
• Strony: 249-273

Daty

wydano

2006

Twórcy

autor

Camillo Trapani

• Dipartimento di Matematica ed Applicazioni, Università di Palermo, I-90123 Palermo, Italy

Identyfikatory

DOI

10.4064/sm172-3-4