Related papers: Uniformly convex renormings and generalized cotype…

We analyze the quantum capacity of a unital quantum channel, using ideas from the proof of near-optimality of Petz recovery map [Barnum and Knill 2000] and give an upper bound on the quantum capacity in terms of regularized output $2$-norm…

We obtain Gabor frame characterisations of modulation spaces defined via a class of translation-modulation invariant Banach spaces of distributions that was recently introduced in $[10]$. We show that these spaces admit an atomic…

It is shown that if (X, ||.||_X) is a Banach space with Rademacher cotype q then for every integer n there exists an even integer m< n^{1+1/q}$ such that for every f:Z_m^n --> X we have $\sum_{j=1}^n \Avg_x [ ||f(x+ (m/2) e_j)-f(x) ||_X^q ]…

We study the problem of totally smooth renormings of Banach spaces and provide such renormings for spaces which are weakly compactly generated. We also consider renormings for $(a,B,c)$-ideals.

In this paper we show sharp lower bounds for norms of even homogeneous Fourier multipliers in $\mathcal L(L^p(\mathbb R^d; X))$ for $1<p<\infty$ and for a UMD Banach space $X$ in terms of the range of the corresponding symbol. For example,…

For Banach spaces of analytic functions on the disc for which the polynomials are dense and their pointt evaluations continuous, we prove the following: If they contain a function such that the limit superior of its modulus is infinite…

Modifying the moduli of supporting convexity and supporting smoothness, we introduce new moduli for Banach spaces which occur, e.g., as lengths of catheti of right-angled triangles (defined via so-called quasi-orthogonality). These…

We prove that the norm of $X\widehat{\otimes}_\pi Y$ is SSD if either $X=\ell_p(I)$ for $p>2$ and $Y$ is a finite-dimensional Banach space such that the modulus of convexity is of power type $q<p$ (e.g. if $Y^*$ is a subspace of $L_q$) or…

The aim of this note is to complement and extend some recent results on Whitley's indices of thinness and thickness in three main directions. Firstly, we investigate both the indices when forming $\ell_p$-sums of Banach spaces, and obtain…

We show that there are sampling projections on arbitrary $n$-dimensional subspaces of $B(D)$ with at most $2n$ samples and norm of order $\sqrt{n}$, where $B(D)$ is the space of complex-valued bounded functions on a set $D$. This gives a…

We prove that for every Banach space $Y$, the Besov spaces of functions from the $n$-dimensional Euclidean space to $Y$ agree with suitable local approximation spaces with equivalent norms. In addition, we prove that the Sobolev spaces of…

We prove a conjecture of Colmez concerning the reduction modulo $p$ of invariant lattices in irreducible admissible unitary $p$-adic Banach space representations of $GL_2(Q_p)$ with $p\ge 5$. This enables us to restate nicely the $p$-adic…

A reflexive Banach space with an unconditional basis admits an equivalent $1$-unconditional $2R$ norm and embeds into a reflexive space with a $1$-symmetric $2R$ norm. Partial results on $1$-symmetric $2R$ renormings of spaces with a…

We show that the renormalized volume of a quasifuchsian hyperbolic 3-manifold is equal, up to an additive constant, to the volume of its convex core. We also provide a precise upper bound on the renormalized volume in terms of the…

Let $G$ be a connected reductive group over a totally real field $F$ which is compact modulo center at archimedean places. We find congruences modulo an arbitrary power of p between the space of arbitrary automorphic forms on $G(\mathbb…

We investigate the existence of equivalent p-norms, 0< p 1, under which conditional symmetric or spreading bases in quasi-Banach spaces become isometric. For spreading bases (which need not be unconditional or even Schauder bases), we…

The renormalized volume is a smooth function associating to every convex co-compact hyperbolic $3$-manifold $M$ a real number. When the boundary of $M$ is incompressible, the renormalized volume is always positive, otherwise there are…

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…

It is well known that every convex body in a finite dimensional normed space can be uniformly approximated by strictly convex and smooth convex bodies. However, in the case of infinite dimensions, little progress has been made since Klee…

For the moduli space of unmarked convex $\mathbb{RP}^2$ structures on the surface $S_{g,m}$ with negative Euler characteristic, we investigate the subsets of the moduli space defined by the notions like boundedness of projective invariants,…