Linear spaces with small generated subspaces

Subspaces of de Branges spaces generated by majorants

For a given deBranges space H(E) we investigate deBranges subspaces defined in terms of majorants on the real axis: If ω is a nonnegative function on R, we consider the subspace Rω(E) = ClosH(E) { F ∈ H(E) : ∃C > 0 : |EF | ≤ Cω on R } . We show that Rω(E) is a deBranges subspace and describe all subspaces of this form. Moreover, we give a criterion for the existence of positive minimal majorant...

Linear spaces with many small lines

In this paper some of the work in linear spaces in which most of the lines have few points is surveyed. This includes existence results, blocking sets and embeddings. Also, it is shown that any linear space of order c can be embedded in a linear space of order about 13v in which there are no lines of size 2.

Totally Isotropic Subspaces of Small Height in Quadratic Spaces

Let K be a global field or Q, F a nonzero quadratic form on KN , N ≥ 2, and V a subspace of KN . We prove the existence of an infinite collection of finite families of small-height maximal totally isotropic subspaces of (V, F ) such that each such family spans V as a K-vector space. This result generalizes and extends a well known theorem of J. Vaaler [16] and further contributes to the effecti...

Subspaces of Small Codimension of Finite-dimensional Banach Spaces

Given a finite-dimensional Banach space E and a Euclidean norm on E, we study relations between the norm and the Euclidean norm on subspaces of E of small codimension. Then for an operator taking values in a Hubert space, we deduce an inequality for entropy numbers of the operator and its dual. In this note we study the following problem: given an n-dimensional Banach space E and a Euclidean no...

ε-weakly Chebyshev subspaces and quotient spaces