Generalized quasi-Banach sequence spaces and measures of noncompactness

Generalized quasi-Banach sequence spaces and measures of noncompactness

Given 0 < s ≤ 1 and ψ an s-convex function, s – ψ -sequence spaces are introduced. Several quasi-Banach sequence spaces are thus characterized as a particular case of s – ψ -spaces. For these spaces, new measures of noncompactness are also defined, related to the Hausdorff measure of noncompactne...

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Bibliographic Details
Main Authors: EDUARDO B. SILVA, DIOCESAR L. FERNANDEZ, LUDMILA NIKOLOVA
Format: Article
Language:English
Published: Academia Brasileira de Ciências 2013-06-01
Series:Anais da Academia Brasileira de Ciências
Subjects:
espacos quase-Banach
funcoes quase-convexas
medidas de nao compacidade
teoria de interpolacao
Online Access:http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652013000200443&lng=en&tlng=en
Description
Summary:Given 0 < s ≤ 1 and ψ an s-convex function, s – ψ -sequence spaces are introduced. Several quasi-Banach sequence spaces are thus characterized as a particular case of s – ψ -spaces. For these spaces, new measures of noncompactness are also defined, related to the Hausdorff measure of noncompactness. As an application, compact sets in s – ψ -interpolation spaces of a quasi-Banach couple are studied.
ISSN:1678-2690

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