A real p-homogeneous seminorm with square property is submultiplicative

TL;DR

This paper proves that certain p-homogeneous seminorms with the square property on real associative algebras are submultiplicative, using a functional representation theorem for real p-Banach algebras.

Contribution

It introduces a functional representation theorem for real p-Banach algebras and applies it to establish submultiplicativity of p-homogeneous seminorms with the square property.

Findings

p-homogeneous seminorms with square property are submultiplicative

Functional representation theorem for real p-Banach algebras established

Application to real associative algebras

Abstract

We give a functional representation theorem for a class of real p-Banach algebras. This theorem is used to show that every p-homogeneous seminorm with square property on a real associative algebra is submultiplicative.