Related papers: Bourgain-uo sequential completeness in vector latt…

Burzyk, Kli\'{s} and Lipecki proved that every topological vector space (tvs) $E$ with the property $(K)$ is a Baire space. K\c{a}kol and S\'{a}nchez Ruiz proved that every sequentially complete Fr\'{e}chet--Urysohn locally convex space…

We prove the following results: (i) Every absolutely weakly compact set in a Banach lattice is absolutely weakly sequentially compact. (ii) The converse of (i) holds if $E$ is separable or $B_{E^{**}}$ is absolutely weak$^*$ compact. (iii)…

In this paper, considering a real Banach sequence lattice Y instead of a Lebesgue sequence space $l_p$ we generalize p-convexity of a linear operator $T:E\to X$, where E is a Banach space and X is a Banach lattice. Then we prove that basic…

This paper is devoted to providing a unifying approach to the study of the uniqueness of unconditional bases, up to equivalence and permutation, of infinite direct sums of quasi-Banach spaces. Our new approach to this type of problem…

We study uO convergence on infinitely distributive lattices, extending key properties known from Riesz spaces. We show that order continuity of uO convergence characterizes infinite distributivity. We examine O-adherence and uO adherence of…

We show that every Banach space in which weakly compact sets are super weakly compact in automatically weakly sequentially complete answering a question by Silber (2024). In the proof we show how to build a weakly compact set which is not…

We prove maximal Schauder regularity for solutions to elliptic systems and Cauchy problems, in the space $C_b(\mathbb{R}^d;\mathbb{R}^m)$ of bounded and continuous functions, associated to a class of nonautonomous weakly coupled…

A net $(x_\gamma)_{\gamma\in\Gamma}$ in a locally solid Riesz space $(X,\tau)$ is said to be unbounded $\tau$-convergent to $x$ if $|x_\gamma-x|\wedge u\mathop{\overset{\tau}{\longrightarrow}} 0$ for all $u\in X_+$. We recall that there is…

The essence of the notion of lineability and spaceability is to find linear structures in somewhat chaotic environments. The existing methods, in general, use \textit{ad hoc} arguments and few general techniques are known. Motivated by the…

For $X = \mathbb{P}^n$ the Euler sequence is given by $$ 0 \rightarrow \Omega^1_{\mathbb{P}^n} \rightarrow \mathcal{O}_{\mathbb{P}^n}^{n+1}(-1) \rightarrow \mathcal{O}_{\mathbb{P}^n} \rightarrow 0 $$ We describe the Lagrangian cobordism…

We show that a free vector lattice over a real vector space $V$ can be realised canonically as a vector lattice of real-valued positively homogeneous functions on any linear subspace of its dual space that separates the points of $V$. This…

We construct a Bourgain-Delbaen $\mathscr{L}_\infty$-space $\mathfrak{X}_{Kus}$ with strongly heterogenous structure: any bounded operator on $\mathfrak{X}_{Kus}$ is a compact perturbation of a multiple of the identity, whereas the space…

Suppose $X$ is a locally solid vector lattice. In this paper, we introduce the notion "$AM$-property" in $X$ as an extension for $AM$-spaces in the category of all Banach lattices. With the aid of this concept, we characterize spaces in…

The main subject of this paper is the analysis of sequences of exponentially bounded integrated semigroups which are related to Cauchy problems \begin{equation}\label{jed} \frac{\partial}{\partial t}u(t,x)-a(D)u(t,x)=f(t,x), \quad…

We investigate some topics related to the celebrated Baker-Campbell-Hausdorff Theorem: a non-convergence result and prolongation issues. Given a Banach algebra $\mathcal{A}$ with identity $I$, and given $X,Y\in \mathcal{A}$, we study the…

We study two classes of linear difference differential equations analogous to Euler-Cauchy ordinary differential equations, but in which multiple arguments are shifted forward or backward by fixed amounts. Special cases of these equations…

First-order jet bundles can be put at the foundations of the modern geometric approach to nonlinear PDEs, since higher-order jet bundles can be seen as constrained iterated jet bundles. The definition of first-order jet bundles can be given…

A real valued function defined on a subset $E$ of $\mathbb{R}$, the set of real numbers, is $\rho$-statistically downward continuous if it preserves $\rho$-statistical downward quasi-Cauchy sequences of points in $E$, where a sequence…

The Bohr-Bohnenblust-Hille Theorem states that the width of the strip in the complex plane on which an ordinary Dirichlet series $\sum_n a_n n^{-s}$ converges uniformly but not absolutely is less than or equal to 1/2, and this estimate is…

In these notes, we study nonlinear embeddings between Banach spaces which are also weakly sequentially continuous. In particular, our main result implies that if a Banach space $X$ coarsely (resp. uniformly) embeds into a Banach space $Y$…