相关论文: On the definition of some Banach spaces over bound…

Separation bounds are a fundamental measure of the complexity of solving a zero-dimensional system as it measures how difficult it is to separate its zeroes. In the positive dimensional case, the notion of reach takes its place. In this…

This paper systematically investigates a new geometric constant associated with isosceles orthogonality in Banach spaces. By establishing the connection between this new constant and a classical function, sharp upper and lower bounds for…

We present some properties of orthogonality and relate them with support disjoint and norm inequalities in p Schatten ideals. In addition, we investigate the problem of characterization of norm parallelism for bounded linear operators. We…

We show that there exists a Banach space in which every non-empty weakly open subset of its unit ball has radius one, the maximum possible value, but the infimum of the diameter of its slices is exactly one, so extremely far from its…

In this note, we study the geometry of the unit ball of the Banach space generated by the adequate family of all subsets of branches of the infinite binary tree, and answer several open questions related to slicely countably determined…

We show that a C*-algebra is a $1$-separably injective Banach space if, and only if, it is linearly isometric to the Banach space $C_0(\Omega)$ of complex continuous functions vanishing at infinity on a substonean locally compact Hausdorff…

The Hardy-Littlewood-P\'{o}lya inequality of majorization is extended to the framework of ordered Banach spaces. Several applications illustrating our main results are also included.

Assuming the generalized continuum hypothesis we construct arbitrarily big indecomposable Banach spaces. i.e., such that whenever they are decomposed as $X\oplus Y$, then one of the closed subspaces $X$ or $Y$ must be finite dimensional. It…

We prove that for a domain $\Omega \subset \mathbb{R}^n$, being $(\epsilon,\delta)$ in the sense of Jones is equivalent to being an extension domain for bmo$(\Omega)$, the nonhonomogeneous version of the space of function of bounded mean…

We show some results related to the classical Banach-Tarski paradox in the setting of finite-dimensional normed spaces over a non-Archimedean valued field $K$. For instance, all balls and spheres in $K^n$, and the whole space $K^n$ (for…

Several recent papers investigated unbounded convergences in Banach lattices. Combine all unbounded convergences, including unbounded order (norm, absolute weak, absolute weak*) convergence, we characterize L-weakly compact sets, L-weakly…

A sufficient condition for $\bar{\partial}$ to have closed range is given for pseudoconvex, possibly unbounded domains in $\mathbb{C}^n$.

We define and study the properties of $\gamma^{*}$-regular and $\gamma$-normal spaces. We also continue studying $\gamma_{o}$-compact spaces defined in [5].

We consider linear bounded operators acting in Banach spaces with a basis, such operators can be represented by an infinite matrix. We prove that for an invertible operator there exists a sequence of invertible finite-dimensional operators…

We first define the trace on a domain $\Omega$ which is definable in an o-minimal structure. We then show that every function $u\in W^{1,p}(\Omega)$ vanishing on the boundary in the trace sense satisfies Poincar\'e inequality. We finally…

We prove in particular that Banach spaces of the form $C_0(\Omega)$, where $\Omega$ is a locally compact space, enjoy a quantitative version of the reciprocal Dunford-Pettis property.

We prove some results on weakly almost square Banach spaces and their relatives. On the one hand, we discuss weak almost squareness in the setting of Banach function spaces. More precisely, let $(\Omega,\Sigma)$ be a measurable space, let…

Consider a linear impulsive equation in a Banach space $$\dot{x}(t)+A(t)x(t) = f(t), ~t \geq 0,$$ $$x(\tau_i +0)= B_i x(\tau_i -0) + \alpha_i,$$ with $\lim_{i \rightarrow \infty} \tau_i = \infty $. Suppose each solution of the corresponding…

M. Talagrand showed that, for the Cech-Stone compactification \beta\omega\ of the space of natural numbers, the norm and the weak topology generate different Borel structures in the Banach space C(\beta\omega). We prove that the Borel…

Let $\Omega$ be a bounded symmetric domain except the two exceptional domains of ${\Bbb C}^N$ and $\phi$ a holomorphic self-map of $\Omega.$ This paper gives a sufficient and necessary condition for the composition operator $C_{\phi}$…