Hypercyclic subspaces in Fréchet spaces

Operators with Common Hypercyclic Subspaces

We provide a reasonable sufficient condition for a family of operators to have a common hypercyclic subspace. We also extend a result of the third author and A. Montes [22], thereby obtaining a common hypercyclic subspace for certain countable families of compact perturbations of operators of norm no larger than one.

Bernstein's Lethargy Theorem in Fréchet spaces

In this paper we consider Bernstein’s Lethargy Theorem (BLT) in the context of Fréchet spaces. Let X be an infinite-dimensional Fréchet space and let V = {Vn} be a nested sequence of subspaces of X such that Vn ⊆ Vn+1 for any n ∈ N and X = ⋃∞ n=1 Vn. Let en be a decreasing sequence of positive numbers tending to 0. Under an additional natural condition on sup{dist(x, Vn)}, we prove that there e...

ε-weakly Chebyshev subspaces and quotient spaces

Equiangular subspaces in Euclidean spaces

A set of lines through the origin is called equiangular if every pair of lines defines the same angle, and the maximum size of an equiangular set of lines in R was studied extensively for the last 70 years. In this paper, we study analogous questions for k-dimensional subspaces. We discuss natural ways of defining the angle between k-dimensional subspaces and correspondingly study the maximum s...

Subspaces of Knot Spaces

The inclusion of the space of all knots of a prescribed writhe in a particular isotopy class into the space of all knots in that isotopy class is a weak homotopy equivalence.