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Comparison of Orlicz-Lorentz spaces

S. Montgomery-Smith (1992)

Studia Mathematica

Orlicz-Lorentz spaces provide a common generalization of Orlicz spaces and Lorentz spaces. They have been studied by many authors, including Mastyło, Maligranda, and Kamińska. In this paper, we consider the problem of comparing the Orlicz-Lorentz norms, and establish necessary and sufficient conditions for them to be equivalent. As a corollary, we give necessary and sufficient conditions for a Lorentz-Sharpley space to be equivalent to an Orlicz space, extending results of Lorentz and Raynaud. We...

Complementation in spaces of symmetric tensor products and polynomials.

Fernando Blasco (1996)

Extracta Mathematicae

Our aim here is to announce some properties of complementation for spaces of symmetric tensor products and homogeneous continuous polynomials on a locally convex space E that have, in particular, consequences in the study of the property (BB)n,s recently introduced by Dineen [8].

Complemented copies of c0 in C0(Ω).

Juan Carlos Ferrando, Manuel López Pellicer (2001)

RACSAM

En esta nota consideramos una clase de espacios topológicos de Hausdorff localmente compactos (Ω) con la propiedad de que el espacio de Banach C0(Ω) de todas las funciones continuas con valores escalares definidas en Ω que se anulan en el infinito, equipado con la norma supremo, contiene una copia de C0 norma-uno complementada, mientras que C (βΩ) contiene una copia de l∞ linealmente isométrica.

Complemented copies of c0 in vector-valued Köthe-Dieudonné function spaces.

Santiago Díaz, Antonio Fernandez, Miguel Florencio, Pedro J. Paúl (1992)

Collectanea Mathematica

Let [Lambda] be a barrelled perfect (in the sense of J. Dieudonné) Köthe space of measurable functions defined on an atomless finite Radon measure space. Let X be a Banach space containing a copy of c0, then the space [Lambda(X)] of [Lambda]-Bochner integrable functions contains a complemented copy of c0.

Complete interpolating sequences for Paley-Wiener spaces and Muckenhoupt's (Ap) condition.

Yurii I. Lyubarskii, Kristian Seip (1997)

Revista Matemática Iberoamericana

We describe the complete interpolating sequences for the Paley-Wiener spaces Lπp (1 < p < ∞) in terms of Muckenhoupt's (Ap) condition. For p = 2, this description coincides with those given by Pavlov [9], Nikol'skii [8] and Minkin [7] of the unconditional bases of complex exponentials in L2(-π,π). While the techniques of these authors are linked to the Hilbert space geometry of Lπ2, our method of proof is based in turning the problem into one about boundedness of the Hilbert transform...

Completions of normed algebras of differentiable functions

William J. Bland, Joel F. Feinstein (2005)

Studia Mathematica

We look at normed spaces of differentiable functions on compact plane sets, including the spaces of infinitely differentiable functions considered by Dales and Davie in [7]. For many compact plane sets the classical definitions give rise to incomplete spaces. We introduce an alternative definition of differentiability which allows us to describe the completions of these spaces. We also consider some associated problems of polynomial and rational approximation.

Complétude des noyaux reproduisants dans les espaces modèles

Emmanuel Fricain (2002)

Annales de l’institut Fourier

Soit ( λ n ) n ≥ 1 une suite de Blaschke du disque unité 𝔻 et Θ une fonction intérieure. On suppose que la suite de noyaux reproduisants k Θ ( z , λ n ) : = 1 - Θ ( λ n ) ¯ Θ ( z ) 1 - λ n ¯ z n ≥ 1 est complète dans l’espace modèle K Θ p : = H p ∩ Θ H 0 p ¯ , 1 < p < + ∞ . On étudie, dans un premier temps, la stabilité de cette propriété de complétude, à la fois sous l’effet de perturbations des fréquences ( λ n ) n ≥ 1 mais également sous l’effet de perturbations de la fonction Θ . On retrouve ainsi un certain nombre de résultats classiques sur les systèmes d’exponentielles. Puis, si on suppose de plus que la suite ...

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