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Functionals on Banach Algebras with Scattered Spectra

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Mustafayev H.

Bulletin of the Polish Academy of Sciences. Mathematics

2004

tom 52

nr 4

395-403

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 $A* = \overline{span} M_A$.

The norm spectrum in certain classes of commutative Banach algebras

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Mustafayev H.

Colloquium Mathematicum

2011

tom 123

nr 1

95-114

Let A be a commutative Banach algebra and let $Σ_{A}$ be its structure space. The norm spectrum σ(f) of the functional f ∈ A* is defined by $σ(f) = \overline{f·a: a ∈ A} ∩ Σ_{A}$, where f·a is the functional on A defined by ⟨f·a,b⟩ = ⟨f,ab⟩, b ∈ A. We investigate basic properties of the norm spectrum in certain classes of commutative Banach algebras and present some applications.

Ograniczanie wyników

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 Colloquium Mathematicum

2 Mustafayev H.

1 2011

1 2004

Wyniki wyszukiwania

Functionals on Banach Algebras with Scattered Spectra

The norm spectrum in certain classes of commutative Banach algebras