Scholarlink

This chapter explores the concept of 2-normed groups, which are a generalization of 2-normed spaces, and provides examples of such groups including the discrete Heisenberg group with Python codes for computing the 2-norm on the mentioned group, the group of positive real numbers with multiplication, and the group of integer pairs with addition. The chapter also discusses the properties of 2-normed groups, such as the relationship between the 2-norm and the group operation. Furthermore, this chapter proposes a definition of a 2-Banach group, which is a 2-normed group in which every Cauchy sequence is convergent. The chapter concludes by proving several lemmas and theorems related to 2-normed groups, including the uniqueness of the limit of a convergent sequence and the relationship between the limit of a sequence and its 2-norm.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

2-Normed Groups: Unraveling Computational Properties of 2-Norms

  • 章节

  • 发表日期：

    2025年

查看全文
  • Alireza Pourmoslemi,
  • Tahere Nazari,
  • Mehdi Salimi

摘要

This chapter explores the concept of 2-normed groups, which are a generalization of 2-normed spaces, and provides examples of such groups including the discrete Heisenberg group with Python codes for computing the 2-norm on the mentioned group, the group of positive real numbers with multiplication, and the group of integer pairs with addition. The chapter also discusses the properties of 2-normed groups, such as the relationship between the 2-norm and the group operation. Furthermore, this chapter proposes a definition of a 2-Banach group, which is a 2-normed group in which every Cauchy sequence is convergent. The chapter concludes by proving several lemmas and theorems related to 2-normed groups, including the uniqueness of the limit of a convergent sequence and the relationship between the limit of a sequence and its 2-norm.