相关论文: Pe{\l}czy\'{n}ski's property ($V^{*}$) of order $p…

For $1\leq p\leq q\leq\infty$ and a locally convex space $E$, we introduce and study the $(V^\ast)$ subsets of order $(p,q)$ of $E$ and the $(V)$ subsets of order $(p,q)$ of the topological dual $E'$ of $E$. Using these sets we define and…

A Banach space $X$ has Pe{\l}czy\' nski's property (V) if for every Banach space $Y$ every unconditionally converging operator $T\colon X\to Y$ is weakly compact. In 1962, Aleksander Pe{\l}czy\' nski showed that $C(K)$ spaces for a compact…

We prove that Pelczy\'nski's property (V$^*$) is locally determined for Lipschitz-free spaces, and obtain several sufficient conditions for it to hold. We deduce that $\mathcal{F}(M)$ has property (V$^*$) when the complete metric space $M$…

A Banach space X has Pelczynski's property (V) if for every Banach space Y every unconditionally converging operator T: X -> Y is weakly compact. H. Pfitzner proved that C*-algebras have Pelczynski's property (V). In the preprint "H.…

Let $E$ be a separable Banach space and $\Omega$ be a compact Hausdorff space. It is shown that the space $C(\Omega,E)$ has property (V) if and only if $E$ does. Similar result is also given for Bochner spaces $L^p(\mu,E)$ if $1<p<\infty$…

We generalize the notion of $M$-ideals in order smooth $\infty$-normed spaces to "smooth $p$-order ideals" in order smooth $p$-normed spaces. We show that if $V$ is an order smooth $p$-normed space and $W$ is a closed subspace of $V$, then…

We give new proofs that some Banach spaces have Pe{\l}czy\'nski's property $(V)$.

We introduce the so-called Bishop-Phelps-Bollob\'as property for positive functionals, a particular case of the Bishop-Phelps-Bollob\'as property for positive operators. First we show a version of the Bishop-Phelps-Bollob\'as theorem for…

In this work we shall be concerned with some stability aspects of the classical problem of extension of $C(K)$-valued operators. We introduce the class $\mathscr{LP}$ of Banach spaces of Lindenstrauss-Pe{\l}czy\'{n}ski type as those such…

By using Bernstein-type inequality we define analogs of spaces of entire functions of exponential type in $L_{p}(X), 1\leq p\leq \infty$, where $X$ is a symmetric space of non-compact. We give estimates of $L_{p}$-norms, $1\leq p\leq…

We prove that the class of positive operators from $L_\infty (\mu)$ to $L_1 (\nu)$ has the Bishop-Phelps-Bollob\'as property for any positive measures $\mu$ and $\nu$. The same result also holds for the pair $(c_0, \ell_1)$. We also provide…

By seeing whether a Liouville type theorem holds for positive, bounded, and/or finite energy $p$-harmonic and $p$-quasiharmonic functions, we classify proper metric spaces equipped with a locally doubling measure supporting a local…

In this paper, we discuss various basic properties of moduli of smoothness of functions from $L_p(\mathbb{R}^d)$, $0<p\le \infty$. In particular, complete versions of Jackson-, Marchaud-, and Ulyanov-type inequalities are given for the…

The $p$-Gelfand Phillips property ($1\le p<\infty$) is studied in spaces of operators. Dunford - Pettis type like sets are studied in Banach spaces. We discuss Banach spaces $X$ with the property that every $p$-convergent operator $T:X\to…

The $\Lambda$-sequence spaces $\Lambda_p$ for $1< p\leq\infty$ and its generalization $\Lambda_{\hat{p}}$ for $1<\hat{p}<\infty$, $\hat{p}=(p_n)$ is introduced. The James constants and strong $n$-th James constants of $\Lambda_p$ for…

Given $1<p<N$ and two measurable functions $V\left( r\right) \geq 0$ and $K\left( r\right) >0$, $r>0$, we define the weighted spaces \[ W=\left\{ u\in D^{1,p}(\mathbb{R}^{N}):\int_{\mathbb{R}^{N}}V\left( \left| x\right| \right) \left|…

A locally compact group $G$ is amenable if and only if it has Reiter's property $(P_p)$ for $p=1$ or, equivalently, all $p \in [1,\infty)$, i.e., there is a net $(m_\alpha)_\alpha$ of non-negative norm one functions in $L^p(G)$ such that…

We study the question of which Polish groups can be realized as subgroups of the unitary group of a separable infinite-dimensional Hilbert space. We also show that for a separable unital C$^*$-algebra $A$, the identity component…

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…

We identify the smooth points of $L^1(\mu,X)$, and provide some necessary and sufficient conditions for left and right symmetry of points with respect to Birkhoff-James orthogonality in $L^p(\mu,X), 1\leq p<\infty$, where $\mu$ is any…