Related papers: The reconstruction formula for Banach frames and d…

It is shown that Paley-Wiener functions on Riemannian manifolds of bounded geometry can be reconstructed in a stable way from some countable sets of their inner products with certain distributions of compact support. A reconstruction method…

We prove a sampling theorem for infinite-dimensional Paley-Wiener spaces on graphs which allows for stable frame reconstruction. We prove that all sampling sets for a fixed Paley-Wiener space are complements of lambda-sets (i.e. sets where…

Let N and M be von Neumann algebras. It is proved that L^p(N) does not Banach embed in L^p(M) for N infinite, M finite, 1 < or = p < 2. The following considerably stronger result is obtained (which implies this, since the Schatten p-class…

It is known that a system formed by translates of a single function cannot be an unconditional Schauder basis in the space $L^p(\mathbb{R})$ for any $1 \le p < \infty$. To the contrary, there do exist unconditional Schauder frames of…

In cross-section-space probability table constructions, reaction-channel levels are reconstructed on fixed total-subgroup nodes and probabilities. Although the standard full-matching reconstruction is uniquely determined, it does not in…

We investigate possible quantifications of R. C. James' classical work on bases and reflexivity of Banach spaces. By introducing new quantities measuring how far a basic sequence is from being shrinking and/or boundedly complete, we prove…

We consider signal reconstruction from the norms of subspace components generalizing standard phase retrieval problems. In the deterministic setting, a closed reconstruction formula is derived when the subspaces satisfy certain cubature…

We prove a structural property of the class of unconditionally saturated separable Banach spaces. We show, in particular, that for every analytic set $\aaa$, in the Effros-Borel space of subspaces of $C[0,1]$, of unconditionally saturated…

A remarkable theorem of R. C. James is the following: suppose that $X$ is a Banach space and $C \subseteq X$ is a norm bounded, closed and convex set such that every linear functional $x^* \in X^*$ attains its supremum on $C$; then $C$ is a…

In the first part of the paper we study the structure of Banach spaces with a conditional spreading basis. The geometry of such spaces exhibit a striking resemblance to the geometry of James' space. Further, we show that the averaging…

Let $I\subseteq \Bbb N$ be a finite or infinite set and let ${(x_n)_{n\in I}}$ be a frame for a separable Hilbert space $\mathcal{H}$. Consider transmission of a signal $h\in\mathcal{H}$ where a finite subset $(\langle h,x_n\rangle)_{n\in…

We prove that if every element $u$ in a Hilbert space $H$ admits a representation as unconditionally convergent series $$u=\sum_{k=1}^\infty \langle u, y_k\rangle x_k,$$ then there exist nonzero scalars $\{\alpha_k\}_{k=1}^\infty$ such that…

A necessary and sufficient condition for existence of a Banach space with a finite dimensional decomposition but without the $\pi$-property in terms of norms of compositions of projections is found.

The aim of this paper is to present two tools, Theorems 4 and 7, that make the task of finding equivalent polyhedral norms on certain Banach spaces easier and more transparent. The hypotheses of both tools are based on countable…

We develop a novel and unifying setting for phase retrieval problems that works in Banach spaces and for continuous frames and consider the questions of uniqueness and stability of the reconstruction from phaseless measurements. Our main…

We consider the following problem: given a set $\Lambda \subset \mathbb{R} \times \mathbb{R}$ and $p \neq 2$, does there exist a function $g \in L^p(\mathbb{R})$ such that the Gabor system $\{g(x-t) e^{2 \pi isx}\}$, $(t,s) \in \Lambda$,…

Necessary and sufficient conditions are given for when a sequence of finite dimensional subspaces (X_n) can be blocked to be a skipped blocking decompositon (SBD). These are very similar to known results about blocking of biorthogonal…

Following James' approach, we shall define the Banach space $J(e)$ for each vector $e=(e_1,e_2,...,e_d) \in \Bbb{R}^d$ with $ e_1 \ne 0$. The construction immediately implies that J(1) coincides with the Hilbert space $i_2$ and that…

We give an intrinsic characterisation of the separable reflexive Banach spaces that embed into separable reflexive spaces with an unconditional basis all of whose normalised block sequences with the same growth rate are equivalent. This…

We will show that an unconditional basis in a Banach space is equivalent to the unit vector basis of $c_0$ or $\ell_p$ for $1\le p < \infty$ if and only if all finitely supported blocks of the basis generated by a unit vector and its dual…