Displaying similar documents to “Isometries of finite-dimensional normed spaces.”

A universal modulus for normed spaces

Carlos Benítez, Krzysztof Przesławski, David Yost (1998)

Studia Mathematica

Similarity:

We define a handy new modulus for normed spaces. More precisely, given any normed space X, we define in a canonical way a function ξ:[0,1)→ ℝ which depends only on the two-dimensional subspaces of X. We show that this function is strictly increasing and convex, and that its behaviour is intimately connected with the geometry of X. In particular, ξ tells us whether or not X is uniformly smooth, uniformly convex, uniformly non-square or an inner product space.

Banach spaces and bilipschitz maps

J. Väisälä (1992)

Studia Mathematica

Similarity:

We show that a normed space E is a Banach space if and only if there is no bilipschitz map of E onto E ∖ {0}.

On l^∞ subspaces of Banach spaces.

Patrick N. Dowling (2000)

Collectanea Mathematica

Similarity:

We obtain refinement of a result of Partington on Banach spaces containing isomorphic copies of l-∞. Motivated by this result, we prove that Banach spaces containing asymptotically isometric copies of l-∞ must contain isometric copies of l-∞.

Rotund and uniformly rotund Banach spaces.

V. Montesinos, J. R. Torregrosa (1991)

Collectanea Mathematica

Similarity:

In this paper we prove that the geometrical notions of Rotundity and Uniform Rotundity of the norm in a Banach space are stable for the generalized Banach products.