Continuous characters and joint topological spectrum

• Autorzy: Żelazko W.
• Języki publikacji: EN

Abstrakty

EN

It is well known that there is a one-to-one correspondence between the characters of a finitely generated commutative Banach algebra and the joint spectrum of its generators. In this paper we show that this fact is also true for an arbitrary semitopological algebra and its continuous characters, provided we replace the concept of a joint spectrum by concept of a topological joint spectrum. In particular, we show that a finitely generated semitopological algebra has a continuous character if and only if the topological joint spectrum of its generators is non-void.

Słowa kluczowe

EN

semitopological algebra; character; (joint) topological spectrum; generators

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2007
• Tom: Vol. 36, no 3
• Strony: 859--864
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Żelazko W.

• Mathematical Institute, Polish Academy of Sciences, Śniadeckich 8, PO Box 21, 00-956 Warsaw, Poland,

Bibliografia

• ABEL, M. and ŻELAZKO, W. (2006) Topologically invertible elements and topological spectrum. Bull. Pol. Acad. Sc. Math. 54, 257-271.
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• BIAŁYNICKI-BIRULA, A. and ŻELAZKO, W. (1957) On the multiplicative-linear functionals on the Cartesian product of algebras. Bull. Acad. Polon. Sc. 5, 201-203.
• LARSEN, R. (1973) Banach Algebras. New York.
• MICHAEL, E.A. (1952) Locally Multiplicatively-Convex Topological Algebras. Mem. Amer. Math. Soc. 11.
• ŻELAZKO, W. (1971) Selected Topics on Topological Algebras. Aarhus University Lecture Notes Series 31.