Functionals on Banach algebras with scattered spectra

• Autorzy: Mustafayev H. S.
• Języki publikacji: EN

Abstrakty

EN

Let A be a complex, commutative Banach algebra and let M[A] be the structure space of A. Assume that there exists a continuous homomorphism h : L^1(G) --> A with dense range, where L^1(G) is a group algebra of the locally compact abelian group G. The main results of this note can be summarized as follows: (a) If every weakly almost periodic functional on A with compact spectra is almost periodic, then the space M[A] is scattered (i.e., M[A] has no nonempty perfect subset). (b) Weakly almost periodic functionals on A with compact scattered spectra are almost periodic. (c) If M[A] is scattered, then the algebra A is Arens regular if and only if A* = span M[A].

Słowa kluczowe

EN

Banach algebra; group algebra; (weakly) almost periodic functional; scattered set

PL

algebra Banacha; algebra grupowa; zbiór rozproszony

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: Vol. 52, nr 4
• Strony: 395--403
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Mustafayev H. S.

• Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, F. Agaev St. 9, Baku, Azerbaijan

Bibliografia

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