Related papers: Diameter two properties in James spaces

A Banach space has the weak fixed point property if its dual space has a weak$^*$ sequentially compact unit ball and the dual space satisfies the weak$^*$ uniform Kadec-Klee property; and it has the \fpp if there exists $\epsilon>0$ such…

In this note various geometric properties of a Banach space $X$ are characterized by means of weaker corresponding geometric properties involving an ultrapower $X^\mathcal{U}$. The characterizations do not depend on the particular choice of…

We study almost square Banach spaces under a topological point of view. Indeed, we prove that the class of Banach spaces which admits an equivalent norm to be ASQ is that of those Banach spaces which contain an isomorphic copy of $c_0$. We…

In this work we study three different versions of small diameter properties of the unit ball in a Banach space and its dual. The related concepts for all closed bounded convex sets of a Banach space was initiated and developed in \cite{B3},…

In this work, we study the non rough norms in Banach spaces with small diameter properties, namely the Ball Dentable Property (BDP), the Ball Huskable Property (BHP) and the Ball Small Combination of Slice Property (BSCSP). We introduce two…

We introduce a new topological property called (*) and the corresponding class of topological spaces, which includes spaces with $G_\delta$-diagonals and Gruenhage spaces. Using (*), we characterise those Banach spaces which admit…

In contrast with the separable case, we prove that the existence of almost $L$-orthogonal vectors in a nonseparable Banach space $X$ (octahedrality) does not imply the existence of nonzero vectors in $X^{**}$ being $L$-orthogonal to $X$,…

A vast literature on the theory and phenomenology of Two-Higgs-Doublet models (2HDM) exists since long. However, the present situation demands a revisit of some 2HDM properties. Now that a 125 GeV scalar resonance has been discovered at the…

We prove that Banach spaces $\ell_1\oplus_2\mathbb{R}$ and $X\oplus_\infty Y$, with strictly convex $X$ and $Y$, have plastic unit balls (we call a metric space plastic if every non-expansive bijection from this space onto itself is an…

Let X be a complex Banach space, in this work we characterize the property of Frechet differentiability for the dual space of X. In the following, we show that if the dual space of X is Gateaux differentiable, then the dual space of Lp(X)…

We study the pseudoduality transformations in two dimensional N = (2, 2) sigma models on K\"ahler manifolds. We show that structures on the target space can be transformed into the pseudodual manifolds by means of (anti)holomorphic…

We obtain new progresses about the diameter two property and the Daugavet property in tensor product spaces. Namely, the main results of the paper are: -If $X^*$ has the WODP, then $X\widehat{\otimes}_\varepsilon Y$ has the DD2P for any…

This paper studies strongly local symmetric Dirichlet forms on general measure spaces. The underlying space is equipped with the intrinsic metric induced by the Dirichlet form, with respect to which the metric measure space does not…

A geometry of superspace corresponding to double field theory is developed, with type II supergravity in D=10 as the main example. The formalism is based on an orthosymplectic extension OSp(d,d|2s) of the continuous T-duality group.…

Let $K$ be a compact Hausdorff space and let $H$ be a real or complex Hilbert space with dim$(H_\mathbb{R})\geq 2$. We prove that the space $C(K,H)$ of all $H$-valued continuous functions on $K$, equipped with the supremum norm, satisfies…

We explore new implications of the $M(r,s)$ and $M^*(r,s)$ properties for Banach spaces. We show that a Banach space $X$ satisfying property $M(1,s)$ for some $0<s\leq 1$, admitting a point $x_{0}$ in its unit sphere at which the relative…

A Banach space $X$ has the $2$-summing property if the norm of every linear operator from $X$ to a Hilbert space is equal to the $2$-summing norm of the operator. Up to a point, the theory of spaces which have this property is independent…

We show that string theory on a compact negatively curved manifold, preserving a U(1)^{b_1} winding symmetry, grows at least b_1 new effective dimensions as the space shrinks. The winding currents yield a "D-dual" description of a Riemann…

Associated with every separable Hilbert space $\mathcal{H}$ and a given localized frame, there exists a natural test function Banach space $\mathcal{H}^1$ and a Banach distribution space $\mathcal{H}^{\infty}$ so that $\mathcal{H}^1 \subset…

We study the best coapproximation problem in Banach spaces, by using Birkhoff-James orthogonality techniques. We introduce two special types of subspaces, christened the anti-coproximinal subspaces and the strongly anti-coproximinal…