0
votes
0answers
341 views

Surjectively isometric normed spaces: Hamel vs (extended) Schauder dimension

Bonjour/bonsoir à toutes et à tous. This may really be a very basic question, but... Let $\mathbf{X} \equiv (X, \|\cdot\|_X)$ and $\mathbf{Y} \equiv (Y, \|\cdot\|_Y)$ be surjectively isometric (1) ...
3
votes
2answers
412 views

“Measuring” how far is one Banach space from being surjectively isometric to another

Bonjour/bonsoir à toutes et à tous. Assume that $\mathbf{V} \equiv (V, \|\cdot\|_V)$ and $\mathbf{W} \equiv (W, \|\cdot\|_W)$ are Banach spaces (over the real or complex field). Question 1. What ...
2
votes
1answer
639 views

When do 0-preserving isometries have to be linear?

Let $\langle \mathbf{V},+,\cdot,||.|| \rangle$ be a normed vector space over $\mathbb{R}$. Let $f : \mathbf{V} \to \mathbf{V}$ be an isometry that satisfies $f(\mathbf{0}) = \mathbf{0}$ . What ...