Related papers: Characterization of greedy bases in Banach spaces

The aim of this note is to present two results that make the task of finding equivalent polyhedral norms on certain Banach spaces, having either a Schauder basis or an uncountable unconditional basis, easier and more transparent. The…

Greedy expansions with prescribed coefficients have been introduced by V. N. Temlyakov in the frame of Banach spaces. The idea is to choose a sequence of fixed (real) coefficients $\{c_n\}_{n=1}^\infty$ and a fixed set of elements…

In this paper, a characterization of normed barrelled spaces is given, as well as a similar characterization of rings of sets with the Nikodym Property. Finally, a condition that is equivalent to a Banach space having a separable quotient…

Decomposable dependency models possess a number of interesting and useful properties. This paper presents new characterizations of decomposable models in terms of independence relationships, which are obtained by adding a single axiom to…

In this note, we consider several notions related to the Grothendieck property. Among them, we introduce the notion "unbounded Grothendieck property" in a Banach lattice as an unbounded version of the known Grothedieck property in the…

We introduce a measure of {\em greedy connectivity} for geographical networks (graphs embedded in space) and where the search for connecting paths relies only on local information, such as a node's location and that of its neighbors.…

Rearrangement-invariance in function spaces can be viewed as a kind of generalization of 1-symmetry for Schauder bases. We define subrearrangement-invariance in function spaces as an analogous generalization of 1-subsymmetry. It is then…

Motivated by, e.g., sensitivity analysis and end-to-end learning, the demand for differentiable optimization algorithms has been significantly increasing. In this paper, we establish a theoretically guaranteed versatile framework that makes…

Our goal in this paper is to advance the state of the art of the topic of uniqueness of unconditional basis. To that end we establish general conditions on a pair $(\mathbb{X}, \mathbb{Y})$ formed by a quasi-Banach space $\mathbb{X}$ and a…

A Banach space contains either a minimal subspace or a continuum of incomparable subspaces. General structure results for analytic equivalence relations are applied in the context of Banach spaces to show that if $E_0$ does not reduce to…

Greedy algorithms are widely used for problems in machine learning such as feature selection and set function optimization. Unfortunately, for large datasets, the running time of even greedy algorithms can be quite high. This is because for…

We show that characteristic functions of domains with boundaries transversal to stable cones are bounded multipliers on a recently introduced scale $U^{t,s}_p$ of anisotropic Banach spaces, under the conditions -1+1/p<s<-t<0 and -(r-1)+t<s,…

It was previously known that the almost greedy (AG) property essentially remains the same when we enlarge greedy sums in the classical definition by a factor $\lambda \geqslant 1$. The present paper shows that if instead, we enlarge greedy…

We define a fragment of monadic infinitary second-order logic corresponding to an abstract separation property. We use this to define the concept of a separation subclass. We use model theoretic techniques and games to show that separation…

Let X and Y be separable metrizable spaces, and f:X-->Y be a function. We want to recover f from its values on a small set via a simple algorithm. We show that this is possible if f is Baire class one, and in fact we get a characterization.…

We consider classes of objective functions of cardinality constrained maximization problems for which the greedy algorithm guarantees a constant approximation. We propose the new class of $\gamma$-$\alpha$-augmentable functions and prove…

This article was initially motivated by our goal to show that the Banach space $\mathbb{G}$ constructed by Gowers in [W. T. Gowers, A solution to Banach's hyperplane problem, Bull. London Math. Soc. 26 (1994), no. 6, 523-530] to settle…

In this paper, we establish new advances in the theory started by T. Oikhberg in [15] where the author joins greedy approximation theory with the use of sequences with gaps. Concretely, we address and partially answer three open questions…

This paper introduces and investigates novel properties of uaw-Dunford-Pettis operators on Banach spaces, exploring their relationships with other classes of operators. We further define and characterize new property of Banach lattices.…

This is the first of two closely related papers on transversality. Here we introduce the notion of tangential transversality of two closed subsets of a Banach space. It is an intermediate property between transversality and…