A real seminorm with square property is submultiplicative

TL;DR

This paper proves that any real seminorm with the square property on an associative algebra is necessarily submultiplicative, establishing a key property for such seminorms.

Contribution

It demonstrates that the square property in a real seminorm implies submultiplicativity, clarifying the structure of seminorms on associative algebras.

Findings

Seminorm with square property is submultiplicative

Provides a characterization of seminorms with the square property

Enhances understanding of algebraic seminorm structures

Abstract

A seminorm with square property on a real associative algebra is submultiplicative