相关论文: P-spaces and the Volterra property

We investigate the Whyburn and weakly Whyburn property in the class of $P$-spaces, that is spaces where every countable intersection of open sets is open. We construct examples of non-weakly Whyburn $P$-spaces of size continuum, thus giving…

Let $2\leq p<\infty$ and $X$ be a complex infinite-dimensional Banach space. It is proved that if $X$ is $p$-uniformly PL-convex, then there is no nontrivial bounded Volterra operator from the weak Hardy space…

A $P$-space is a topological space whose every $G_{\delta}$-set is open. In this article, basic properties of $P$-spaces are investigated in the absence of the Axiom of Choice. New weaker forms of the Axiom of Choice, all relevant to…

We investigate connections between resolvability and different forms of tightness. This study is adjacent to [1,2]. We construct a non-regular refinement $\tau^*$ of the natural topology of the real line $\mathbb{R}$ with properties such…

We construct a consistent example of a topological space $Y=X \cup \{\infty\}$ such that: 1) $Y$ is regular. 2) Every $G_\delta$ subset of $Y$ is open. 3) The point $\infty$ is not isolated, but it is not in the closure of any discrete…

In this paper we introduce and study the notion of pairwise weakly Lindelof bitopological spaces and obtain some results. Further, we also study the pairwise weakly Lindelof subspaces and subsets, investigate some of their properties and…

In this article, we study the relationship between \(p\)-\((V)\) subsets and p-\(V^*\) subsets of dual spaces. We investigate the Banach space X with the property that adjoint every \(p\)-convergent operator \(T: X \rightarrow Y\) is weakly…

Given a property $P$ of subspaces of a $T_1$ space $X$, we say that $X$ is {\em $P$-bounded} iff every subspace of $X$ with property $P$ has compact closure in $X$. Here we study $P$-bounded spaces for the properties $P \in \{\omega D,…

We show that the non-compact generalised analytic Volterra operators $T_g$, where $g \in \mathit{BMOA}$, have the following structural rigidity property on the Hardy spaces $H^p$ for $1 \le p < \infty$ and $p \neq 2$: if $T_g$ is bounded…

In our paper [18] we showed that a Tychonoff space $X$ is a $\Delta$-space (in the sense of [20], [30]) if and only if the locally convex space $C_{p}(X)$ is distinguished. Continuing this research, we investigate whether the class $\Delta$…

We study the quasi-nilpotency of generalized Volterra operators on spaces of power series with Taylor coefficients in weighted $\ell^p$ spaces $1<p<+\infty$ . Our main result is that when an analytic symbol $g$ is a multiplier for a…

We introduce notions of nearly good relations and N-sticky modulo a relation as tools for proving that spaces are D-spaces. As a corollary to general results about such relations, we show that C_p(X) is hereditarily a D-space whenever X is…

Orderability, weak orderability and the existence of continuous weak selections on filter spaces (i.e., spaces with a single non-isolated point) and their products are discussed. We prove that a closed continuous image X of a suborderable…

Assume that $\mathcal{P}$ is a topological property of a space $X$, then we say that $X$ is {\it dense-$\mathcal{P}$} if each dense subset of $X$ has the property $\mathcal{P}$. In this paper, we mainly discuss dense subsets of a space $X$,…

We characterize boundedness, compactness and weak compactness of Volterra operators acting between different weighted Banach spaces of entire functions with weighted sup-norms in terms of the symbol g. Thus we complement recent work by…

We introduce a weakened version of the Dunford-Pettis property, and give examples of Banach spaces with this property. In particular, we show that every closed subspace of Schreier's space $S$ enjoys it. As an application, we characterize…

We prove that hereditarily Lindel\"of space which is $F_{\sigma\delta}$ in some compactification is absolutely $F_{\sigma\delta}$. In particular, this implies that any separable Banach space is absolutely $F_{\sigma\delta}$ when equipped…

Let $X$ be a Hausdorff space and let $\mathcal{H}$ be one of the hyperspaces $CL(X)$, $\mathcal{K}(X)$, $\mathcal{F}(X)$ or $\mathcal{F}_n(X)$ ($n$ a positive integer) with the Vietoris topology. We study the following disconnectedness…

Certain operator algebras A on a Hilbert space have the property that every densely defined linear transformation commuting with A is closable. Such algebras are said to have the closability property. They are important in the study of the…

We show that all finite powers of a Hausdorff space X do not contain uncountable weakly separated subspaces iff there is a c.c.c poset P such that 1_P forces that ``X is a countable union of 0-dimensional subspaces of countable weight.'' We…