Related papers: PLB-spaces of holomorphic functions with logarithm…
The existence of a Banach limit as a translation invariant positive continuous linear functional on the space of bounded scalar sequences which is equal to 1 at the constant sequence (1,1,...,1,...) is proved in a first course on functional…
The paper investigates free and projective ${\bf L}$-spaces, where ${\bf L}$ is a given normed space. These spaces form a far-reaching generalization of known $p$-multinormed spaces; in particular, if ${\bf L}=L_p(X)$, the ${\bf L}$-spaces…
In this paper we begin the study of some important Banach spaces of slice hyperholomorphic functions, namely the Bloch, Besov and weighted Bergman spaces, and we also consider the Dirichlet space, which is a Hilbert space. The importance of…
We establish that the category of Silva spaces, aka LS-spaces, formed by countable inductive limits of Banach spaces with compact linking maps as objects and linear and continuous maps as morphisms, is not an integral category. The result…
Finite dimensional subspaces spanned by exponential functions in the space of square integrable functions on a finite interval of the real line are considered. Their limiting positions are studied and described in terms of expo-polynomials.
Many of the known complemented subspaces of L_p have realizations as sequence spaces. In this paper a systematic approach to defining these spaces which uses partitions and weights is introduced. This approach gives a unified description of…
We prove that weakly unconditionally Cauchy (w.u.C.) series and unconditionally converging (u.c.) series are preserved under the action of polynomials or holomorphic functions on Banach spaces, with natural restrictions in the latter case.…
In this paper, we study spaceability of subsets of generalized Orlicz and Lebesgue spaces associated to Banach function space. Also, we give some sufficient conditions for spaceability of subsets of a general Banach space which improves an…
We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the…
We establish an explicit characterisation of L\'evy measures on both $L^p$-spaces and UMD Banach spaces. In the case of $L^p$-spaces, L\'evy measures are characterised by an integrability condition, which directly generalises the known…
We determine the boundedness and compactness of a large class of operators, mapping from general Banach spaces of holomorphic functions into a particular type of spaces of functions determined by the growth of the functions, or the growth…
An algebra of bounded linear operators on a Banach space is said to be {\em strongly compact} if its unit ball is precompact in the strong operator topology, and a bounded linear operator on a Banach space is said to be {\em strongly…
The goal of this note is to prove that every real-valued Lipschitz function on a Banach space can be pointwise approximated on a given $\sigma$-compact set by smooth cylindrical functions whose asymptotic Lipschitz constants are controlled.…
The paper considers a global version of the notion of log canonical threshold for plurisubharmonic functions $u$ of logarithmic growth in $\mathbb{C}^n$, aiming at description of the range of all $p>0$ such that $e^{-u}\in…
We provide a framework for proofs of structural theorems about sets with positive Banach logarithmic density. For example, we prove that if $A\subseteq \mathbb{N}$ has positive Banach logarithmic density, then $A$ contains an approximate…
We establish in this paper a new form of Pl\"unnecke-type inequalities for ergodic probability measure-preserving actions of any countable abelian group. Using a correspondence principle for product sets, this allows us to deduce lower…
We study the existence and the non-existence of frequently hypercyclic subspaces in Banach spaces. In particular, we give an example of a weighted shift on lp possessing a frequently hypercyclic subspace and an example of a frequently…
There are two main aims of the paper. The first one is to extend the criterion for the precompactness of sets in Banach function spaces to the setting of quasi-Banach function spaces. The second one is to extend the criterion for the…
Given a continuous, radial, rapidly decreasing weight $v$ on the complex plane $\mathbf{C}$, we study the solid hull of its associated weighted space $H_v^\infty(\mathbf{C})$ of all the entire functions $f$ such that $v|f|$ is bounded. The…
We characterize the restrictions of B\'ekoll\'e--Bonami weights of bounded hyperbolic oscillation, to subsets of the unit disc, thus proving an analogue of Wolff's restriction theorem for Muckenhoupt weights. Sundberg proved a discrete…