Isometries and Linearity

Resonance

article

Rajendra Bhatia¹ 

[1] Ashoka University

关键词: Isometries;    linearity;    Mazur–Ulam theorem;    inner product spaces;    additive functions.;   

DOI  :  10.1007/s12045-022-1448-5

学科分类：社会科学、人文和艺术（综合）

来源: Springer

【 摘 要 】

Let $f$ be a transformation on the Euclidean space such that $f(0) = 0$, and $f$ preserves distances. Then $f$ is linear, and this makes it easier to analyze $f$. The Mazur--Ulam theorem generalizes this to maps between real normed linear spaces. We discuss this theorem and its proofs.

【 授权许可】

Others