Ultrasymmetric sequence spaces in approximation theory.

Título inglés	Ultrasymmetric sequence spaces in approximation theory.
Título español	Espacios ultrasimétricos de sucesiones en teoría de la aproximación.
Autor/es	Pustylnik, Evgeniy
Organización	Dep. Math. Tech. Israel Inst. Technol., Haifa, Israel
Revista	0010-0757
Publicación	2006, 57 (3): 257-277, 14 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	Let φ(t) be a positive increasing function and let Ê be an arbitrary sequence space, rearrangement-invariant with respect to the atomic measure µ(n) = 1/n. Let {an*} mean the decreasing rearrangement of a sequence {|an|}. A sequence space lφ,E with symmetric (quasi)norm || {φ(n)an*} ||Ê is called ultrasymmetric, because it is not only intermediate but also interpolation between the corresponding Lorentz and Marcinkiewicz spaces Λφ and Mφ. We study properties of the spaces lφ,E for all admissible parameters φ, E and use them for the definition of ultrasymmetric approximation spaces Xφ,E, which essentially generalize most of classical approximation spaces. At the same time we show that the spaces Xφ,E possess almost all properties of classical prototypes, such as equivalent norms, representation, reiteration, embeddings, transformation etc. Special attention is paid to interpolation properties of these spaces. At last, we apply our results to ultrasymmetric operator ideals.
Clasificación UNESCO	120202
Palabras clave español	Teoría de la aproximación ; Espacio de sucesiones ; Espacios de interpolación ; Ideal de operadores ; Espacios lineales normados
Código MathReviews	MR2264322
Código Z-Math	Zbl 1104.41020
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