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Symmetric Banach *-algebras: invariance of spectrum

Bruce Barnes (2000)

Studia Mathematica

Let A be a Banach *-algebra which is a subalgebra of a Banach algebra B. In this paper, assuming that A is symmetric, various conditions are given which imply that A is inverse closed in B.

The C * -algebra of a Hilbert bimodule

Sergio Doplicher, Claudia Pinzari, Rita Zuccante (1998)

Bollettino dell'Unione Matematica Italiana

Un C * -modulo hilbertiano destro X su una C * -algebra A dotato di uno * -omomorfismo isometrico ϕ : A L A X viene qui considerato come un oggetto X A della C * -categoria degli A -moduli Hilbertiani destri. Come in [11], associamo ad esso una C * -algebra O X A contenente X come un « A -bimodulo hilbertiano in O X A ». Se X è pieno e proiettivo finito O X A è la C * -algebra C * X , la generalizzazione delle algebre di Cuntz-Krieger introdotta da Pimsner [27] (e in un caso particolare da Katayama [31]). Più in generale, C * X è canonicamente immersa...

The canonical test case for the non-commutative Singer-Wermer conjecture

Marc P. Thomas (2009)

Studia Mathematica

It is a famous conjecture that every derivation on each Banach algebra leaves every primitive ideal of the algebra invariant. This conjecture is known to be true if, in addition, the derivation is assumed to be continuous. It is also known to be true if the algebra is commutative, in which case the derivation necessarily maps into the (Jacobson) radical. Because I. M. Singer and J. Wermer originally raised the question in 1955 for the case of commutative Banach algebras, the conjecture is...

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