Hypo-q-Norms on a Cartesian Product of Normed Linear Spaces

TL;DR

This paper introduces hypo-q-norms on Cartesian products of normed spaces, providing their representations, equivalence with q-norms, and reverse inequalities using classical inequalities.

Contribution

It presents the novel concept of hypo-q-norms, their representations, and establishes their equivalence with existing q-norms, along with related inequalities.

Findings

Representation of hypo-q-norms via bounded linear functionals

Equivalence between hypo-q-norms and q-norms on Cartesian products

Derived reverse inequalities using classical inequalities

Abstract

In this paper we introduce the hypo-q-norms on a Cartesian product of normed linear spaces. A representation of these norms in terms of bounded linear functionals of norm less than one, the equivalence with the q-norms on a Cartesian product and some reverse inequalities obtained via the scalar Shisha-Mond, Birnacki et al. and other Gruss type inequalities are also given.