Almost Euclidean Quotient Spaces of Subspaces of a Finite-Dimensional Normed Space

Almost Euclidean Quotient Spaces of Subspaces of a Finite-dimensional Normed Space

The main result of this article is Theorem 1 which states that a quotient space Y, dim Y = k, of a subspace of any finite dimensional normed space X, dim X — n, may be chosen to be J-isomorphic to a euclidean space even for k = [Xn] for any fixed X < 1 (and d depending on X only). The following theorem is proved. 1. Theorem. For every d > 1 there exists X(d) > 0 such that every n-dimensional no...

Euclidean Structure in Finite Dimensional Normed Spaces

On the Dimension of Almost Hilbertian Subspaces of Quotient Spaces

The question of the dimension of almost Hilbertian subspaces is resolved in [1] where it is shown that every Banach space E of dimension n possesses almost Hilbertian subspaces of dimension c(logn), where c is an absolute constant, and that this estimate is the best possible. When the net is spread wider to include quotient spaces and subspaces of quotient spaces we should expect to find instan...

ε-weakly Chebyshev subspaces and quotient spaces

Quotients of Finite-dimensional Quasi-normed Spaces

We study the existence of cubic quotients of finite-dimensional quasi-normed spaces, that is, quotients well isomorphic to `∞ for some k. We give two results of this nature. The first guarantees a proportional dimensional cubic quotient when the envelope is cubic; the second gives an estimate for the size of a cubic quotient in terms of a measure of nonconvexity of the quasi-norm.