Related papers: Quantitative Grothendieck Property

For a compact group $\mathbb{G}$, the functor from unital Banach algebras with contractive morphisms to metric spaces with 1-Lipschitz maps sending a Banach algebra $A$ to the space of $\mathbb{G}$-representations in $A$ preserves filtered…

It is shown that for a locally compact group $G$, if $L^{1}(G)^{**}$ is approximately weakly amenable, then $M(G)$ is approximately weakly amenable. Then, new notions of approximate weak amenability and approximate cyclic amenability for…

We investigate possible quantifications of Banach-Saks sets and weak Banach-Saks sets of higher orders and their relations to other quantities. We prove a quantitative version of the characterization of weak $\xi$-Banach-Saks sets using…

Following Davie's example of a Banach space failing the approximation property [D], we show how to construct a Banach space E which is asymptotically Hilbertian and fails the approximation property. Moreover, the space E is shown to be a…

We introduce the notion of asymptotic coarse Lipschitz equivalence of metric spaces. We show that it is strictly weaker than coarse Lipschitz equivalence. We study its impact on the asymptotic dimension of metric spaces. Then we focus on…

In this paper we show that every sequence (F_n) of finite dimensional subspaces of a real or complex Banach space with increasing dimensions can be ``refined'' to yield an F.D.D. (G_n), still having increasing dimensions, so that either…

We show that the dual of every infinite-dimensional Lipschitz-free Banach space contains an isometric copy of $\ell_\infty$ and that it is often the case that a Lipschitz-free Banach space contains a $1$-complemented subspace isometric to…

The celebrated Josefson-Nissenzweig theorem implies that for a Banach space $C(K)$ of continuous real-valued functions on an infinite compact space $K$ there exists a sequence of Radon measures $\langle\mu_n\colon\ n\in\omega\rangle$ on $K$…

With every locally compact group $G$, one can associate several interesting bi-invariant subspaces $X(G)$ of the weakly almost periodic functions $\mathrm{WAP}(G)$ on $G$, each of which captures parts of the representation theory of $G$.…

We characterize non-reflexive Banach spaces by a low-distortion (resp. isometric) embeddability of a certain metric graph up to a renorming. Also we study non-linear sufficient conditions for $\ell_1^n$ being $(1+\varepsilon)$-isomorphic to…

A function space, $L^{\theta,\infty)}(\Omega)$, $0 \leq \theta <\infty$, is defined. It is proved that $L^{\theta,\infty)}(\Omega)$ is a Banach space which is a generalization of exponential class. An alternative definition of…

A typical result in this note is that if $X$ is a Banach space which is a weak Asplund space and has the $\omega^*$-$\omega$-Kadets Klee property, then $X$ is already an Asplund space.

We give a new proof of a recent characterization by Diaz and Mayoral of compactness in the Lebesgue-Bochner spaces $L_X^p$, where $X$ is a Banach space and $1\le p<\infty$, and extend the result to vector-valued Banach function spaces…

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…

We study the properties of "generic", in the sense of the Haar measure on the corresponding Grassmann manifold, subspaces of l^N_infinity of given dimension. We prove that every "well bounded" operator on such a subspace, say E, is a…

In this paper, we study several variants of Hahn-Banach smoothness, viz., property-$(SU)$/$(HB)$/$(wU)$, where property-$(SU)$ and property-$(HB)$ are stronger notions and property-$(wU)$ is a weaker notion of Hahn-Banach smoothness. We…

In this paper we discuss symmetrically self-dual spaces, which are simply real vector spaces with a symmetric bilinear form. Certain subsets of the space will be called q-positive, where q is the quadratic form induced by the original…

We study the general measures of non-compactness defined on subsets of a dual Banach space, their associated derivations and their $\omega$-iterates. We introduce the notions of convexifiable and sublinear measure of non-compactness and…

Let $\msp$ be a purely non-atomic measure space, and let $1 < p < \infty$. If $\weakLp\msp$ is isomorphic, as a Banach space, to $\weakLp\mspp$ for some purely atomic measure space $\mspp$, then there is a measurable partition $\Omega =…

We introduce notions of finite presentation and co-exactness which serve as qualitative and quantitative analogues of finite-dimensionality for operator modules over completely contractive Banach algebras. With these notions we begin the…