Densely ball remotal subspaces of C(K)

On simultaneously remotal sets in spaces of vector-valued functions

In this paper we formulate the notions of simultaneously remotal and that of simultaneously densely remotal sets. We exhibit large classes of Banach spaces which have subspaces, whose unit ball is a simultaneously remotal set. We also study them in spaces of vectorvalued function spaces.

On the Proximinality of the Unit Ball of Proximinal Subspaces in Banach Spaces: a Counterexample

A known, and easy to establish, fact in Best Approximation Theory is that, if the unit ball of a subspace G of a Banach space X is proximinal in X, then G itself is proximinal in X. We are concerned in this article with the reverse implication, as the knowledge of whether the unit ball is proximinal or not is useful in obtaining information about other problems. We show, by constructing a count...

An Effective Contraction Estimate in the Stable Subspaces of Phase Points in Hard Ball Systems

In this paper we prove the following result, useful and often needed in the study of the ergodic properties of hard ball systems: In any hard ball system, for any phase point x0 ∈ M \ ∂M with a non-singular forward orbit Sx0 and with infinitely many consecutive, connected collision graphs on Sx0, and for any number L > 0 one can always find a time t > 0 and a non-zero tangent vector (δq0, δv0) ...

Comment on frame's of subspaces

Covering of subspaces by subspaces

Lower and upper bounds on the size of a covering of subspaces in the Grassmann graph Gq(n, r) by subspaces from the Grassmann graph Gq(n, k), k ≥ r , are discussed. The problem is of interest from four points of view: coding theory, combinatorial designs, q-analogs, and projective geometry. In particular we examine coverings based on lifted maximum rank distance codes, combined with spreads and...