Restricted version of Grand Lebesgue Spaces

Abstract

We introduce a so-called restricted, in particular, discrete version of (Banach) Grand Lebesgue Spaces (GLS), investigate its properties and derive the conditions of coincidence with the classical ones. We show also that these spaces forms also a Banach algebra relative the convolution operation on the unimodular local compact topological group equipped with Haar's measure, alike in the complete GLS case.