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The triangle inequality for graded real vector spaces

Songpon Sriwongsa, Keng Wiboonton

Abstract

In this paper, we prove that a natural candidate for a homogeneous norm on a graded Lie algebra of any length satisfies the triangle inequality which answers Moskowitz's question.

The triangle inequality for graded real vector spaces

Abstract

In this paper, we prove that a natural candidate for a homogeneous norm on a graded Lie algebra of any length satisfies the triangle inequality which answers Moskowitz's question.

Paper Structure

This paper contains 3 sections, 3 theorems, 16 equations.

Table of Contents

  1. Introduction
  2. Proof of the main theorem
  3. Acknowledgements

Key Result

Theorem 1

$\left\lVert X + Y\right\rVert \leq \left\lVert X\right\rVert + \left\lVert Y\right\rVert$ for $r \geq 1$.

Theorems & Definitions (3)

  • Theorem 1
  • Lemma 2
  • Corollary 3