Functionals on Banach Algebras with Scattered Spectra

• Autorzy: H. S. Mustafayev
• 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 $A* = \overline{span} M_A$.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: 52
• Numer: 4
• Strony: 395-403

Daty

wydano

2004

Twórcy

autor

H. S. Mustafayev

• 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

Identyfikatory

DOI

10.4064/ba52-4-5