A normal Banach quasi -algebra (X;A_0) 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 fi nite spectral radius. If the family P(X) of bounded invariant positive sesquilinear forms on X contains suffi ciently many elements then the Banach -algebra of bounded elements can be characterized via a C -seminorm defi ned by the elements of P(X).

TRAPANI, C. (2006). Banach elements and spectrum in Banach quasi *-algebras. STUDIA MATHEMATICA, 172, 249-273 [10.4064/sm172-3-4].

Banach elements and spectrum in Banach quasi *-algebras

TRAPANI, Camillo
2006-01-01

Abstract

A normal Banach quasi -algebra (X;A_0) 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 fi nite spectral radius. If the family P(X) of bounded invariant positive sesquilinear forms on X contains suffi ciently many elements then the Banach -algebra of bounded elements can be characterized via a C -seminorm defi ned by the elements of P(X).
2006
TRAPANI, C. (2006). Banach elements and spectrum in Banach quasi *-algebras. STUDIA MATHEMATICA, 172, 249-273 [10.4064/sm172-3-4].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/23358
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