Related papers: Slope filtration on Banach-Colmez spaces

This article gives a new proof of the fundamental lemma of the "weakly admissible implies admissible" theorem of Colmez-Fontaine that describes the semi-stable p-adic representations. To this end, we introduce the category of spectral…

We show that, given a Banach space and a generator of an exponentially stable $C_{0}$-semigroup, a weakly admissible operator $g(A)$ can be defined for any $g$ bounded, analytic function on the left half-plane. This yields an (unbounded)…

In this article, we apply the methods of our work on Fontaine's theory in equal characteristics to the $\varphi/\mathfrak S$-modules of Breuil and Kisin. Thanks to a previous article of Kisin, this yields a new and rather elementary proof…

We develop the analog in equal positive characteristic of Fontaine's theory for crystalline Galois representations of a p-adic field. In particular we describe the analog of Fontaine's functor which assigns to a crystalline Galois…

The notion of a p-adic de Rham representation of the absolute Galois group of a p-adic field was introduced about twenty years ago (see e.g. [Fo93]). Three important results for this theory have been obtained recently: The structure theorem…

The notions of $p$-convexity and concavity are fundamental tools for studying Banach lattices, as they partition the class of Banach lattices into a scale of spaces with $L_p$-like properties. Upper and lower $p$-estimates provide a…

This paper is concerned with frame decompositions of $\alpha$-modulation spaces. These spaces can be obtained as coorbit spaces for square-integrable representations of the affine Weyl-Heisenberg group modulo suitable subgroups. The theory…

A theorem of Davis, Figiel, Johnson and Pe{\l}czy\'nski tells us that weakly-compact operators between Banach spaces factor through reflexive Banach spaces. The machinery underlying this result is that of the real interpolation method,…

Constructing or learning a function from a finite number of sampled data points (measurements) is a fundamental problem in science and engineering. This is often formulated as a minimum norm interpolation problem, regularized learning…

The question is addressed of when a Sobolev type space, built upon a general rearrangement-invariant norm, on an $n$-dimensional domain, is a Banach algebra under pointwise multiplication of functions. A sharp balance condition among the…

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…

Building on recent work of Ardakov and Wadsley, we prove Schur's lemma for absolutely irreducible admissible p-adic Banach space (respectively locally analytic) representations of p-adic Lie groups. We also prove finiteness results for the…

The concept of a profile decomposition formalizes concentration compactness arguments on the functional-analytic level, providing a powerful refinement of the Banach-Alaoglu weak-star compactness theorem. We prove existence of profile…

We prove a zig-zag conjecture describing the reductions of irreducible crystalline two-dimensional representations of $G_{{\mathbb{Q}}_p}$ of slope $\frac{3}{2}$ and exceptional weights. This along with previous works completes the…

We study the class of compact convex subsets of a topological vector space which admits a strictly convex and lower semicontinuous function. We prove that such a compact set is embeddable in a strictly convex dual Banach space endowed with…

We study linear control systems in infinite--dimensional Banach spaces governed by analytic semigroups. For $p\in[1,\infty]$ and $\alpha\in\RR$ we introduce the notion of $L^p$--admissibility of type $\alpha$ for unbounded observation and…

In \cite[\S1.3]{Br2}, some unitary representations of ${\rm GL}_2(\mathbf{Q}_p)$ on $p$-adic Banach spaces are associated to 2-dimensional irreducible crystalline representations of ${\rm Gal}(\bar{\mathbf{Q}}_p)/\mathbf{Q}_p)$. Some…

Using the game approach to fragmentability, we give new and simpler proofs of the following known results: (a) If the Banach space admits an equivalent Kadec norm, then its weak topology is fragmented by a metric which is stronger than the…

We give a functional representation theorem for a class of real p-Banach algebras. This theorem is used to show that every p-homogeneous seminorm with square property on a real associative algebra is submultiplicative.

In this note the following version of Phillips' lemma is proved. The L-projection of an L-embedded space - that is of a Banach space which is complemented in its bidual such that the norm between the two complementary subspaces is additive…