Related papers: Rethinking Polyhedrality for Lindenstrauss Spaces

In this paper we define a Rokhlin property for automorphisms of non-unital C*-algebras and for endomorphisms. We show that the crossed product of a C*-algebra by a Rokhlin automorphism preserves absorption of a strongly self-absorbing…

Let $H$ be an infinite-dimensional complex Hilbert space and let ${\mathcal G}_{\infty}(H)$ be the set of all closed subspaces of $H$ whose dimension and codimension both are infinite. We investigate (not necessarily surjective)…

Let X be quasi-isometric to either the mapping class group equipped with the word metric, or to Teichmuller space equipped with either the Teichmuller metric or the Weil-Petersson metric. We introduce a unified approach to study the coarse…

We prove the equivalence of two seemingly very different ways of generalising Rademacher's theorem to metric measure spaces. One such generalisation is based upon the notion of forming partial derivatives along a very rich structure of…

In this two-part paper, we review, and then develop, the assessment of the hole argument for general relativity. This first Part reviews the literature hitherto, focussing on the philosophical aspects. It also introduces two main ideas we…

Let C be a separable unital C*-algebra, not isomorphic to the complex numbers, equipped with a faithful tracial state. Let A be a unital direct limit of one dimensional NCCW complexes, also equipped with a faithful tracial state. Suppose…

In 1989, G. Godefroy proved that a Banach space contains an isomorphic copy of $\ell_1$ if and only if it can be equivalently renormed to be octahedral. It is known that octahedral norms can be characterized by means of covering the unit…

The aim of this note is to obtain results about when the norm of a projective tensor product is strongly subdifferentiable. We prove that if $X\hat{\otimes}_\pi Y$ is strongly subdifferentiable and either $X$ or $Y$ has the metric…

A dual pair formulation for asymmetric locally convex spaces is developed that strictly generalises the ordinary vector space setting. The concept of a polar topology carries over to the asymmetric case and some familiar results are…

We show that for a $\sigma $-ideal $\ci$ with a Steinhaus property defined on Banach space, if two non-homeomorphic Banach with the same cardinality of the Hamel basis then there is a $\ci$ nonmeasurable subset as image by any isomorphism…

The present paper contributes to the ongoing programme of quantification of isomorphic Banach space theory focusing on Pe{\l}czy\'nski's classical work on dual Banach spaces containing $L_{1}$ ($=L_{1}[0,1]$) and the Hagler--Stegall…

We discussed some properties of a family of symmetric spaces, namely $\mathcal{P}(n):=SL(n,\mathbb{R})/SO(n,\mathbb{R})$, where we replace the Riemannian metric on $\mathcal{P}(n)$ with a premetric suggested by Selberg. These properties are…

We show that there exists a strong uniform embedding from any proper metric space into any Banach space without cotype. Then we prove a result concerning the Lipschitz embedding of locally finite subsets of $\mathcal{L}_{p}$-spaces. We use…

We study some structural aspects of the subspaces of the non-commutative (Haagerup) L_p-spaces associated with a general (non necessarily semi-finite) von Neumann algebra A. If a subspace X of L_p(A) contains uniformly the spaces \ell_p^n,…

Let P be a locally finite disk pattern on the complex plane C whose combinatorics are described by the one-skeleton G of a triangulation of the open topological disk and whose dihedral angles are equal to a function \Theta:E\to [0,\pi/2] on…

In [Rie08], the second author defined a Landau-Ginzburg model for homogeneous spaces G/P. In this paper, we reformulate this LG model in the case of the odd-dimensional quadric X=Q_{2m-1}. Namely we introduce a regular function Wcan on a…

The famous Rosenthal-Lacey theorem asserts that for each infinite compact set $K$ the Banach space $C(K)$ admits a quotient which is either a copy of $c$ or $\ell_{2}$. What is the case when the uniform topology of $C(K)$ is replaced by the…

We prove that each non-metrizable sequential rectifiable space $X$ of countable $cs^*$-character contains a clopen rectifiable submetrizable $k_\omega$-subspace $H$ and admits an open disjoint cover by subspaces homeomorphic to clopen…

We introduce an algebraic version of the Katsura $C^*$-algebra of a pair $A,B$ of integer matrices and an algebraic version of the Exel-Pardo $C^*$-algebra of a self-similar action on a graph. We prove a Graded Uniqueness Theorem for such…

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…