A Bollobás-type theorem for affine subspaces

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

Pseudoframe multiresolution structure on abelian locally compact groups

‎Let $G$ be a locally compact abelian group‎. ‎The concept of a generalized multiresolution structure (GMS) in $L^2(G)$ is discussed which is a generalization of GMS in $L^2(mathbb{R})$‎. ‎Basically a GMS in $L^2(G)$ consists of an increasing sequence of closed subspaces of $L^2(G)$ and a pseudoframe of translation type at each level‎. ‎Also‎, ‎the construction of affine frames for $L^2(G)$ bas...

The Bishop – Phelps – Bollobás property for numerical radius in ` 1 ( C ) by Antonio

We show that the set of bounded linear operators from X to X admits a Bishop–Phelps–Bollobás type theorem for numerical radius whenever X is `1(C) or c0(C). As an essential tool we provide two constructive versions of the classical Bishop–Phelps– Bollobás theorem for `1(C).

Beurling Dimension of Gabor Pseudoframes for Affine Subspaces

Pseudoframes for subspaces have been recently introduced by S. Li and H. Ogawa as a tool to analyze lower dimensional data with arbitrary flexibility of both the analyzing and the dual sequence. In this paper we study Gabor pseudoframes for affine subspaces by focusing on geometrical properties of their associated sets of parameters. We first introduce a new notion of Beurling dimension for dis...

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...