相关论文: Perturbation of farthest points in weakly compact …

Let $X_1, \dots, X_n$ be Banach spaces and $f$ a real function on $X=X_1 \times\dots \times X_n$. Let $A_f$ be the set of all points $x \in X$ at which $f$ is partially Fr\' echet differentiable but is not Fr\' echet differentiable. Our…

the main goal of this paper is to prove that any Banach space X, that every dual ball in X** is weak* -separable, or every weak* -closed convex subset in X** is weak* -separable, or every norm-closed convex set in X* is constructible,…

For any non-trivial convex and bounded subset $C$ of a Banach space, we show that outside of a $\sigma$-porous subset of the space of non-expansive mappings $C\to C$, all mappings have the maximal Lipschitz constant one witnessed locally at…

Let $X$ and $Y$ be separable Banach spaces. Suppose $Y$ either has a shrinking basis or $Y$ is isomorphic to $C(2^\mathbb{N})$ and $A$ is a subset of weakly compact operators from $X$ to $Y$ which is analytic in the strong operator…

For a Banach space $X$ by $Conv_H(X)$ we denote the space of non-empty closed convex subsets of $X$, endowed with the Hausdorff metric. We prove that for any closed convex set $C\subset X$ and its metric component $H_C=\{A\in…

An upper mean here is a subadditive functional $\overline M$ defined on bounded functions on a commutative group which has, beside some natural requirements, the property we call restricted additivity: if $g(x)= f(x)+f(x+t)$, then…

We conjecture that whenever $M$ is a metric space of density at most continuum, then the space of Lipschitz functions is $w^*$-separable. We prove the conjecture for several classes of metric spaces including all the Banach spaces with a…

If a separable Banach space $X$ is such that for some nonquasireflexive Banach space $Y$ there exists a surjective strictly singular operator $T:X\to Y$ then for every countable ordinal $\alpha $ the dual of $X$ contains a subspace whose…

Let $E$ be a real vector space with dual space $E^*$ and let $C\subset E$ be a convex subset with more than one point. Let $f : C\to\mathbb{R}$ be a function satisfying a mild stability property at 'flat' points of the (relative) boundary…

Let $X$ be a Hausdorff topological vector space, $X^*$ its topological dual and $Z$ a subset of $X^*$. In this paper, we establish some results concerning the $\sigma(X,Z)$-approximate fixed point property for bounded, closed convex subsets…

Given a Banach space we consider the $\sigma$-ideal of all of its subsets which are covered by countably many hyperplanes and investigate its standard cardinal characteristics as the additivity, the covering number, the uniformity, the…

Let $X$ be a real or complex Banach space and $T_t:X\to X$ is a power bounded operator (or a $C_0$-semigroup). If there exists a "occasionally" attracting compact subset K (for each x$ in unit ball $\liminf_n \rho(T^n x, K)=0$ then there…

It is consistent that the continuum be arbitrary large and no absolute $\kappa$-Borel set $X$ of density $\kappa$, $\aleph_1<\kappa<\mathfrak{c}$, condenses onto a compact metric space. It is consistent that the continuum be arbitrary large…

In this paper, we present some necessary and sufficient conditions for semi-compact operators being almost L-weakly compact (resp. almost M-weakly compact) and the converse. Mainly, we prove that if $X$ is a nonzero Banach space, then every…

In this paper we prove that if $X $ is a Banach space, then for every lower semi-continuous bounded below function $f, $ there exists a $\left(\varphi_1, \varphi_2\right)-$convex function $g, $ with arbitrarily small norm, such that $f + g…

Let $k$ be a field, $V$ a $k$-vector space and $X$ be a subset of $V $. A function $f:X\to k$ is weakly polynomial of degree $\leq a$, if the restriction of $f$ on any affine subspace $L\subset X$ is a polynomial of degree $\leq a$. In this…

We introduce the notion of numerical (strong) peak function and investigate the denseness of the norm and numerical peak functions on complex Banach spaces. Let $A_b(B_X:X)$ be the Banach space of all bounded continuous functions $f$ on the…

We construct a Banach space satisfying that the nearest point map (also called proximity mapping or metric projection) onto any compact and convex subset is continuous but not uniformly continuous. The space we construct is locally…

Let $Z$ and $X$ be Banach spaces. Suppose that $X$ is Asplund. Let $\mathcal{M}$ be a bounded set of operators from $Z$ to $X$ with the following property: a bounded sequence $(z_n)_{n\in \mathbb{N}}$ in $Z$ is weakly null if, for each $M…

First we prove that if a separable Banach space $X$ contains an isometric copy of an infinite-dimensional space $A(S)$ of affine continuous functions on a Choquet simplex $S$, then its dual $X^*$ lacks the weak$^*$ fixed point property for…