Weighted algebras of continuous functions

Oubbi, L.

doi:10.1007/bf03322338

Cited by 21 publications

(23 citation statements)

References 8 publications

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“…In the scalar case, the local A -convexity of CV (0) (X) is equivalent to the existence of a l. m. c. topology on CV (0) (X) stronger than the weighted topology [18]. In the vector -valued case, we have Pro o f .…”

Section: Max (P (ϕ(T)ψ(t)) P (ψ(T)ϕ(t))) ≤ M P (ψ(T))mentioning

confidence: 93%

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Weighted Algebras of Vector-Valued Continuous Functions

Oubbi¹

2000

Math. Nachr.

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Section: Max (P (ϕ(T)ψ(t)) P (ψ(T)ϕ(t))) ≤ M P (ψ(T))mentioning

confidence: 93%

“…However, only few authors have considered these spaces as algebras. In [18] (also see [19,20]), a systematic study of the algebras CV (0) (X) was given. But up to now, such a study fails for the vector -valued spaces CV (0) (X, E) introduced in [3].…”

Section: Introductionmentioning

confidence: 99%

Weighted Algebras of Vector-Valued Continuous Functions

Oubbi¹

2000

Math. Nachr.

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“…The problem of establishing if a weighted space of functions is an algebra was considered by L. Oubbi in [58] for weighted spaces of continuous functions. In that setting, CV (X) is an algebra if and only if for every v ∈ V there are C > 0 and…”

Section: On Hv (U ) As An Algebra and Its Spectrum In [25 Propositimentioning

confidence: 99%

On the spectra of algebras of analytic functions

Carando¹,

Garcı́a²,

Maestre³

et al. 2012

Contemporary Mathematics

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Abstract. In this paper we survey the most relevant recent developments on the research of the spectra of algebras of analytic functions. We concentrate mainly in three algebras, the Banach algebra H ∞ (B) of all bounded holomorphic functions on the unit ball B of a complex Banach space X, the Banach algebra of the ball Au(B), and the Fréchet algebra H b (X) of all entire functions bounded on bounded sets.

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“…Different types of Nachbin algebras have been studied for example in [9,10,20,21,22]. Their importance is based on their connections to many classical results on function and topological algebras.…”

Section: Letmentioning

confidence: 99%

Generalization of the topological algebra (C_b(X), β)

Arhippainen

Kauppi

2009

Studia Math.

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Abstract. We study subalgebras of C b (X) equipped with topologies that generalize both the uniform and the strict topology. In particular, we study the Stone-Weierstrass property and describe the ideal structure of these algebras.1. Introduction. Let X be a completely regular Hausdorff space. The algebra C b (X) of all continuous and bounded complex-valued functions on X is one of the most studied objects in modern analysis. Usually it is equipped with the supremum norm topology (denoted by σ) which makes it a Banach algebra. However, the structure of (C b (X), σ) is quite complicated. For example, its Gelfand space (the set of all regular maximal ideals equipped with the relative weak * -topology) is homeomorphic to the Stone-Čech compactification β(X) of X. Another difficulty is that (C b (X), σ) does not have the Stone-Weierstrass property, i.e., a point-separating symmetric subalgebra which is bounded away from zero is not necessarily uniformly dense in C b (X). So the topology on C b (X) defined by the supremum norm is not the "best" topology from this point of view.Another well-known and useful topology on C b (X) is the so-called strict topology (denoted by β) defined by the family of weighted supremum seminorms with weights running through all bounded (or equivalently, upper semicontinuous) non-negative functions on X which vanish at infinity. The topological algebra (C b (X), β) is in some sense easier to handle than (C b (X), σ). For example, its Gelfand space is homeomorphic to X and it has the Stone-Weierstrass property. On the other hand, even though the structure of (C b (X), β) has been extensively studied, it appears that its closed ideals have not been described yet. In [23] it was claimed without proof that in the case when X is locally compact, every closed ideal of (C b (X), β) consists of those functions on C b (X) which vanish on some closed subset E of X.

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Weighted algebras of continuous functions

Cited by 21 publications

References 8 publications

Weighted Algebras of Vector-Valued Continuous Functions

Weighted Algebras of Vector-Valued Continuous Functions

On the spectra of algebras of analytic functions

Generalization of the topological algebra (C_b(X), β)

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Weighted algebras of continuous functions

Cited by 21 publications

References 8 publications

Weighted Algebras of Vector-Valued Continuous Functions

Weighted Algebras of Vector-Valued Continuous Functions

On the spectra of algebras of analytic functions

Generalization of the topological algebra (Cb(X), β)

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Generalization of the topological algebra (C_b(X), β)