相关论文: Countable Tightness and the Grothendieck Property …

We extend Pisier's abstract version of Grothendieck's theorem to general non-locally convex quasi-Banach spaces. We also prove a related result on factoring operators through a Banach space and apply our results to the study of…

This paper addresses the Asplund property for the space of continuous functions $C_k(X)$ equipped with the compact-open topology, when $X$ is an arbitrary Tychonoff space. Motivated by inconsistent definitions in prior literature extending…

For any topological space there is a sheaf cohomology. A Grothendieck topology is a generalization of the classical topology such that it also possesses a sheaf cohomology. On the other hand any noncommutative $C^*$-algebra is a…

In the first part of our note we prove that every Weakly Lindel\"of Determined (WLD) (in particular, every reflexive) non-separable Banach $X$ space contains two dense linear subspaces $Y$ and $Z$ that are not densely isomorphic. This means…

While the theory of matrix-weighted function spaces is well established, the majority of previous results in the infinite-dimensional operator-valued setting deal with "no go" theorems, showing the impossibility of some prospective…

We study a noncommutative version of the infinitesimal site of Grothendieck. A theorem of Grothendieck establishes that the cohomology of the structure sheaf on the infinitesimal topology of a scheme of characteristic zero is de Rham…

The class of spaces such that their product with every Lindel\"of space is Lindel\"of is not well-understood. We prove a number of new results concerning such productively Lindel\"of spaces with some extra property, mainly assuming the…

This paper is devoted to tangent martingales in Banach spaces. We provide the definition of tangency through local characteristics, basic $L^p$- and $\phi$-estimates, a precise construction of a decoupled tangent martingale, new estimates…

A classical theorem of Hurewicz characterizes spaces with the Hurewicz covering property as those having bounded continuous images in the Baire space. We give a similar characterization for spaces X which have the Hurewicz property…

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)…

We investigate preservation of the Lindel\"of property of topological spaces under forcing extensions. We give sufficient conditions for a forcing notion to preserve several strengthenings of the Lindel\"of property, such as indestructible…

We present a reflexive Banach space with an unconditional basis which is quasi-minimal and tight by range, i.e. of type (4) in Ferenczi-Rosendal list within the framework of Gowers' classification program of Banach spaces, but contrary to…

We give several topological/combinatorial conditions that, for a filter on $\omega$, are equivalent to being a non-meager $\mathsf{P}$-filter. In particular, we show that a filter is countable dense homogeneous if and only if it is a…

Building on results of Medvedev, we construct a $\mathsf{ZFC}$ example of a non-Polish topological group that is countable dense homogeneous. Our example is a dense subgroup of $\mathbb{Z}^\omega$ of size $\mathfrak{b}$ that is a…

In this paper, we characterize invertible Toeplitz products on a number of Banach spaces of analytic functions, including weighted Bergman space $L^p_a (\mathbb{B}_n, dv_\gamma)$, the Hardy space $H^p(\partial \mathbb{D})$, and the weighted…

M. Beiglb\"ock, V. Bergelson, and A. Fish proved that if $G$ is a countable amenable group and $A$ and $B$ are subsets of $G$ with positive Banach density, then the product set $AB$ is piecewise syndetic. This means that there is a finite…

The celebrated Josefson-Nissenzweig theorem implies that for a Banach space $C(K)$ of continuous real-valued functions on an infinite compact space $K$ there exists a sequence of Radon measures $\langle\mu_n\colon\ n\in\omega\rangle$ on $K$…

We prove that the countable product of lines contains a Borel linear subspace $L\ne\mathbb R^\omega$ that cannot be covered by countably many closed Haar-meager sets. This example is applied to studying the interplay between various classes…

In this article we proved so-called strong reflection principles corresponding to formal theories Th which has omega-models. An posible generalization of the Lob's theorem is considered.Main results is: (1) let $k$ be an inaccessible…

Let X be a separable metric space and let \beta be the strict topology on the space of bounded continuous functions on X, which has the space of \tau-additive Borel measures as a continuous dual space. We prove a Banach-Dieudonne\'{e} type…