Related papers: $k-$smoothness on polyhedral Banach spaces

We study symmetric points with respect to $(\rho_+)$-orthogonality, $(\rho_{-})$-orthogonality and $\rho$-orthogonality in the space $C(K, \mathbb{X}),$ where $K$ is a perfectly normal, compact space and $ \mathbb X$ is a Banach space. We…

The paper presents a generalization of Arnold-Falk-Winther elements for three dimensional linear elasticity, to meshes with elements of variable order. The generalization is straightforward but the stability analysis involves a non-trivial…

We show that if $X$ and $Y$ are Banach spaces, where $Y$ is separable and polyhedral, and if $T:X \to Y$ is a bounded linear operator such that $T^*(Y^*)$ contains a boundary $B$ of $X$, then $X$ is separable and isomorphic to a polyhedral…

We study left symmetric and right symmetric elements in the space $\ell_{\infty}(K, \mathbb{X}) $ of bounded functions from a non-empty set $K$ to a Banach space $\mathbb{X}.$ We prove that a non-zero element $ f \in\ell_{\infty}(K,…

We construct a version of differential $K$-theory based on smooth Banach manifold models for the homotopy types $B \mathrm U\times Z$ and $\mathrm U$ that appear in the topological $K$-theory spectrum. These manifolds carry natural…

We consider the problem of whether there is a sequence of homeomorphisms $(F_k)_k$ between the unit spheres of the $k$-dimensional Banach spaces $\ell_\infty^k$ and $\ell_1^k$ which is also equi-uniformly continuous. We prove that this…

We show that a variant of a function defined by Cholamjiak and Suantai can be used to characterize 2-uniform smoothness. We then obtain greatly simplified proofs of a convergence theorem of Marino and Xu and of one of Zhou using a…

Let $T$ be a bounded linear operator on a (real or complex) Banach space $X$. If $(a_n)$ is a sequence of non-negative numbers tending to 0. Then, the set of $x \in X$ such that $\|T^nx\| \geqslant a_n \|T^n\|$ for infinitely many $n$'s has…

We investigate different possiblities of subspaces of the space $\ell_{\infty}$ in terms of whether the subspaces are polyhedral or not. We further study finite-dimensional subspaces of $\ell_{\infty}$ which are of the form $\ell_\infty^n$…

We study the relationship between the point-wise symmetry of Birkhoff-James orthogonality and the geometry of the space of operators $\mathbb{B}(\ell_\infty^n,\ell_1^m)$. We show that any non-zero left-symmetric point in this space is a…

We show that norms on certain Banach spaces $X$ can be approximated uniformly, and with arbitrary precision, on bounded subsets of $X$ by $C^{\infty}$ smooth norms and polyhedral norms. In particular, we show that this holds for any…

We consider real spaces only. Definition. An operator $T:X\to Y$ between Banach spaces $X$ and $Y$ is called a Hahn-Banach operator if for every isometric embedding of the space $X$ into a Banach space $Z$ there exists a norm-preserving…

The goal of this note is to prove that every real-valued Lipschitz function on a Banach space can be pointwise approximated on a given $\sigma$-compact set by smooth cylindrical functions whose asymptotic Lipschitz constants are controlled.…

In this paper, we study {\it operator spaces\/} in the sense of the theory developed recently by Blecher-Paulsen [BP] and Effros-Ruan [ER1]. By an operator space, we mean a closed subspace $E\subset B(H)$, with $H$ Hilbert. We will be…

We study ergodicity of composition operators on rearrangement-invariant Banach function spaces. More precisely, we give a natural and easy-to-check condition on the symbol of the operator which entails mean ergodicity on a very large class…

For a Banach space $B$ of functions which satisfies for some $m>0$ $$ \max(\|F+G\|_B,\|F-G\|_B) \ge (\|F\|^s_B + m\|G\|^s_B)^{1/s}, \forall F,G\in B \ (*) $$ a significant improvement for lower estimates of the moduli of smoothness…

We prove that an onto isometry between unit spheres of finite-dimensional polyhedral Banach spaces extends to a linear isometry of the corresponding spaces.

We prove sharp upper bounds on the entropy numbers $e_k(S^{d-1}_p,\ell_q^d)$ of the $p$-sphere in $\ell_q^d$ in the case $k \geq d$ and $0< p \leq q \leq \infty$. In particular, we close a gap left open in recent work of the second author,…

We show the existence of a compact metric space $K$ such that whenever $K$ embeds isometrically into a Banach space $Y$, then any separable Banach space is linearly isometric to a subspace of $Y$. We also address the following related…

We introduce the notion of approximate norm attainment set of a bounded linear operator between Banach spaces and use it to obtain a complete characterization of smooth points in the space of compact linear operators, provided the domain…