Related papers: Characterization of greedy bases in Banach spaces

In this note we extend the notion of greedy bases developed by Lee, Li, and Zelevinsky to rank two generalized cluster algebras, i.e. binomial exchange relations are replaced by polynomial exchange relations. In the process we give a…

Democracy functions of wavelet admissible bases are computed for weighted Orlicz Spaces in terms of its fundamental function. In particular, we prove that these bases are greedy if and only if the Orlicz space is a Lebesgue space. Also,…

Functions in Hardy spaces on multiply-connected domains in the plane are given an explicit characterization in terms of a boundary condition inspired by the two-dimensional Ising model. The key underlying property is the positivity of a…

We prove that the sequence spaces $\ell_p\oplus\ell_q$ and the spaces of infinite matrices $\ell_p(\ell_q)$, $\ell_q(\ell_p)$ and $(\bigoplus_{n=1}^\infty \ell_p^n)_{\ell_q}$, which are isomorphic to certain Besov spaces, have an almost…

We introduce a new class of quasi-Banach spaces as an extension of the classical Grand Lebesgue Spaces for small values of the parameter, and we investigate some its properties, in particular, completeness, fundamental function, operators…

A novel and detailed convergence analysis is presented for a greedy algorithm that was previously introduced for operator reconstruction problems in the field of quantum mechanics. This algorithm is based on an offline/online decomposition…

We show that the Lindenstrauss basic sequence in l_1 may be used to construct a conditional quasi-greedy basis of l_1, thus answering a question of Wojtaszczyk. We further show that the sequence of coefficient functionals for this basis is…

We obtain new uniqueness theorems for harmonic functions defined on the unit disc or in the half plane. These results are applied to obtain new resolvent descriptions of spectral subspaces of polynomially bounded groups of operators on…

A reflexive Banach space with an unconditional basis admits an equivalent $1$-unconditional $2R$ norm and embeds into a reflexive space with a $1$-symmetric $2R$ norm. Partial results on $1$-symmetric $2R$ renormings of spaces with a…

We characterize non-reflexive Banach spaces by a low-distortion (resp. isometric) embeddability of a certain metric graph up to a renorming. Also we study non-linear sufficient conditions for $\ell_1^n$ being $(1+\varepsilon)$-isomorphic to…

We prove that if the squares of two unconditional bases are equivalent up to a permutation, then the bases themselves are permutatively equivalent. This settles a twenty year-old question raised by Casazza and Kalton in [Uniqueness of…

If a Banach space has an unconditional basis it either contains a continuum of non isomorphic subspaces or is isomorphic to its square and hyperplanes and satisfies other regularity properties. An HI Banach space contains a continuum of non…

In the setting of Banach lattices the weak (resp. positive) Grothendieck spaces have been defined. We localize such notions by defining new classes of sets that we study and compare with some quite related different classes. This allows us…

We study the new basis of the (complexified) Grothendieck group of unipotent representations of a split reductive group over a finite field. For exceptional types we use a definition of the new basis which differs from the earlier one.

This paper establishes alternative characterizations of very expressive classes of existential rule sets with decidable query entailment. We consider the notable class of greedy bounded-treewidth sets (gbts) and a new, generalized variant,…

Let $(e_i)_i$ denote the unit vector basis of $\ell_p$, $1\leq p< \infty$, or $c_0$. We construct a reflexive Banach space with an unconditional basis that admits $(e_i)_i$ as a uniformly unique spreading model while it has no subspace with…

In terms of fragmentability, we describe a new class of Banach spaces which do not contain weak-G_delta open bounded subsets. In particular, none of these spaces is isomorphic to a separable polyhedral space.

We investigate the existence of equivalent p-norms, 0< p 1, under which conditional symmetric or spreading bases in quasi-Banach spaces become isometric. For spreading bases (which need not be unconditional or even Schauder bases), we…

We prove optimal embeddings for nonlinear approximation spaces in terms of weighted Lorentz sequence spaces, with the weights depending on the democracy functions of the basis. As applications we recover known embeddings for $N$-term…

We introduce an unconditional concept of almost squareness in order to provide a partial negative answer to the problem of existence of any dual almost square Banach space. We also take advantage of this notion to provide some criterion of…