Related papers: Computing the complexity of the relation of isomet…
In these notes, we study the relation between uniform and coarse embeddings between Banach spaces. In order to understand this relation better, we also look at the problem of when a coarse embedding can be assumed to be topological. Among…
We obtain sharp approximation results for into nearisometries between Lp spaces and nearisometries into a Hilbert space. Our main theorem is the optimal approximation result for nearsurjective nearisometries between general Banach spaces.
This paper develops a geometric approach of variational analysis for the case of convex objects considered in locally convex topological spaces and also in Banach space settings. Besides deriving in this way new results of convex calculus,…
This paper deals with the interplay of the geometry of the norm and the weak topology in Banach spaces. Both dual and intrinsic connections between weak forms of rotundity and smoothness ared discussed. Weakly exposed points, weakly locally…
If Z is a quotient of a subspace of a separable Banach space X, and V is any separable Banach space, then there is a Banach couple (A_0,A_1) such that A_0 and A_1 are isometric to $X\oplus V$, and any intermediate space obtained using the…
We study the structure of the Rochberg Banach spaces $\mathfrak Z_n$ associated to the interpolation pair $(\ell_\infty, \ell_1)$ at $1/2$, and the operators defined on them
We investigate the $\mathcal F$-Borel complexity of topological spaces in their different compactifcations. We provide a simple proof of the fact that a space can have arbitrarily many different complexities in different compactifications.…
Similar to ordinary differential equations, rough paths and rough differential equations can be formulated in a Banach space setting. For $\alpha\in (1/3,1/2)$, we give criteria for when we can approximate Banach space-valued weakly…
Given $L$ a complex solvable finite dimensional Lie Algebra of operators acting on a Banach space $E$ and $\{ x_i\}_{1\le i\le n}$ a Jordan-H\"older basis of $ L$, we study the relation between $Sp(L,E)$ and $\Pi Sp(x_i)$.
The absolute logarithmic Weil height is well defined on the group of units of the algebraic closure of the rational numbers, modulo roots of unity, and induces a metric topology on this group. We show that the completion of this metric…
A problem of Banach asks whether every infinite-dimensional Banach space which is isomorphic to all its infinite-dimensional subspaces must be isomorphic to a separable Hilbert space. In this paper we prove a result of a Ramsey-theoretic…
We prove that there exist weakly countably determined spaces of complexity higher than coanalytic. On the other hand, we also show that coanalytic sets can be characterized by the existence of a cofinal adequate family of closed sets.…
We show that the class of Banach algebras that can be isometrically represented on an $L^p$-space, for $p\neq 2$, is not closed under quotients. This answers a question asked by Le Merdy 20 years ago. Our methods are heavily reliant on our…
We introduce the concept of weak L-P property for a pair of Banach spaces, in the study of extreme contractions. We give examples of pairs of Banach spaces (not) satisfying weak L-P property and apply the concept to compute the exact number…
We construct Zachary space in $\R^\infty$ and find that this is a Banach space of functions of bounded mean oscillation with order $p, 1\leq p \leq \infty$ containing the function of bounded mean oscillation $BMO[\R_I^\infty]$ as a dense…
We suggest an approach for description of integrable cases of the Abel equations. It is based on increasing of the order of equations up to the second one and using equivalence transformations for the corresponding second-order ordinary…
We prove in this article that every Borelian measure, for example, the distribution of a random variable, in separable Banach space has a support which is compact embedded Banach subspace; and prove that if the norm of the random variable…
Using three different approaches, we analyze the complexity of various birational maps constructed from simple operations (inversions) on square matrices of arbitrary size. The first approach consists in the study of the images of lines,…
In this paper, we construct a compact subset of the real plane whose path-connectedness equivalence relation is Borel bireducible to a nonsmooth hyperfinite Borel equivalence relation. This answers a question of \cite{bec98}.
We consider countable Borel equivalence relations on quotient Borel spaces. We prove a generalization of the Feldman-Moore representation theorem, but provide some examples showing that other very simple properties of countable equivalence…