Related papers: Polyhedrality for twisted sums with $C(\omega^\alp…

It is shown that all the approximately finite dimensional C*-algebras which are not of Type I are isomorphic as Banach spaces. This generalises the matroid case given previously by Arazy. Analogous results are obtained for various families…

An atomic decomposition is proved for Banach spaces which satisfy some affine geometric axioms compatible with notions from the quantum mechanical measuring process. This is then applied to yield, under appropriate assumptions, geometric…

We prove that, if Banach spaces $X$ and $Y$ are $\delta$-average rough, then their direct sum with respect to an absolute norm $N$ is $\delta/N(1,1)$-average rough. In particular, for octahedral $X$ and $Y$ and for $p$ in $(1,\infty)$ the…

We present an isometric version of the complementably universal Banach space $\mathbb{P}$ with a Schauder decomposition. The space $\mathbb{P}$ is isomorphic to Pe{\l}czy\'nski's space with a universal basis as well as to Kadec'…

Following a result of Hatori, Miura and Tagaki ([4]) we give here a spectral characterization of an isomorphism from a $C^\star$-algebra onto a Banach algebra. We then use this result to show that a $C^\star$-algebra $A$ is isomorphic to a…

We prove that a WLD subspace of the space $\ell_\infty^c(\Gamma)$ consisting of all bounded, countably supported functions on a set $\Gamma$ embeds isomorphically into $\ell_\infty$ if and only if it does not contain isometric copies of…

It is well known that a three dimensional (closed, connected and compact) manifold is obtained by identifying boundary faces from a polyhedron P. The study of (\partial P)/~, the boundary \partial P with the polygonal faces identified in…

We investigate the following general problem, closely related to the problem of isomorphic classification of Banach spaces $C(K)$ of continuous real-valued functions on a compact space $K$, equipped with the supremum norm: Let $\mathcal{K}$…

We introduce and study twisted triangular Banach algebras T_sigma(A,B;X), built from Banach algebras A,B, a Banach A-B bimodule X, and a pair of automorphisms sigma=(sigma_A,sigma_B). This construction extends the classical triangular…

The space of shapes of a polyhedron with given total angles less than 2\pi at each of its n vertices has a Kaehler metric, locally isometric to complex hyperbolic space CH^{n-3}. The metric is not complete: collisions between vertices take…

In this article, we classify (non-compact) $3$-manifolds with uniformly positive scalar curvature. Precisely, we show that an oriented $3$-manifold has a complete metric with uniformly positive scalar curvature if and only if it is…

We show that every Banach space $X$ containing an isomorphic copy of $c_0$ has an infinite equilateral set and also that if $X$ has a bounded biorthogonal system of size $\alpha$ then it can be renormed so as to admit an equilateral set of…

A Banach space E is c_0-saturated if every closed infinite dimensional subspace of E contains an isomorph of c_0. A c_0-saturated Banach space with an unconditional basis which has a quotient space isomorphic to l^2 is constructed.

We show that a C*-algebra is a $1$-separably injective Banach space if, and only if, it is linearly isometric to the Banach space $C_0(\Omega)$ of complex continuous functions vanishing at infinity on a substonean locally compact Hausdorff…

In this paper, we describe geometrical constructions to obtain triangulations of connected sums of closed orientable triangulated 3-manifolds. Using these constructions, we show that it takes time polynomial in the number of tetrahedra to…

It is proved that the relation of isomorphism between separable Banach spaces is a complete analytic equivalence relation, i.e., that any analytic equivalence relation Borel reduces to it. Thus, separable Banach spaces up to isomorphism…

We consider Hecke symmetries on a 3-dimensional vector space with the associated R-symmetric algebra isomorphic to the polynomial algebra $k[x_1,x_2,x_3]$ twisted by an automorphism. The main result states that any such a Hecke symmetry is…

Let $\lambda$ be a large enough cardinal number (assuming GCH it suffices to let $\lambda=\aleph_\omega$). If $X$ is a Banach space with $\text{dens}(X)\ge\lambda$, which admits a coarse (or uniform) embedding into any $c_0(\Gamma)$, then…

Let $X$ be a separable nonquasireflexive Banach space. Let $Y$ be a Banach space isomorphic to a subspace of $X^*$. The paper is devoted to the following questions: 1. Under what conditions does there exist an isomorphic embedding $T:Y\to…

We study linear and algebraic structures in sets of bounded holomorphic functions on the ball which have large cluster sets at every possible point (i.e., every point on the sphere in several complex variables and every point of the closed…