Generalized quasi-Banach sequence spaces and measures of noncompactness

Abstract

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.

Keywords

• espacos quase-Banach
• funcoes quase-convexas
• medidas de nao compacidade
• teoria de interpolacao