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## Bulletin of the Polish Academy of Sciences. Mathematics

2004 | 52 | 4 | 395-403
Tytuł artykułu

### Functionals on Banach Algebras with Scattered Spectra

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Treść / Zawartość
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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:L¹(G) → A with dense range, where L¹(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 $A* = \overline{span} M_A$.
Słowa kluczowe
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
395-403
Opis fizyczny
Daty
wydano
2004
Twórcy
autor
• Department of Mathematics, Faculty of Arts and Sciences, Yuzuncu Yil University, 65080 Van, Turkey
• Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, F. Agaev St. 9, Baku, Azerbaijan
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