Related papers: Projecting onto Helson matrices in Schatten classe…
We consider the difference $f(H_1)-f(H_0)$, where $H_0=-\Delta$ and $H_1=-\Delta+V$ are the free and the perturbed Schr\"odinger operators in $L^2(\mathbb R^d)$, and $V$ is a real-valued short range potential. We give a sharp sufficient…
We prove that the Chebyshev spline orthoprojectors are uniformly bounded on $L^\infty$.
Assuming the continuum hypothesis CH, we obtain complete $*$-isomorphic classification of maximal abelian self-adjoint subalgebras (masas) of the Calkin algebra $\mathcal Q(\ell_2)$ (bounded operators on a separable Hilbert space modulo…
We prove that the Markov-Stieltjes transform is a bounded non compact Hankel operator on Hardy space $H^p$ with Hilbert matrix with respect to the standard Schauder basis of $H^p$ and a bounded non compact operator on Lebesgue space…
We are interested in the normal class of an algebraic hypersurface Z of the complex projective space P^n, that is the number of normal lines to Z passing through a generic point of P^n. Thanks to the notion of normal polar, we state a…
The Bergman projection $P_\alpha$, induced by a standard radial weight, is bounded and onto from $L^\infty$ to the Bloch space $\mathcal{B}$. However, $P_\alpha: L^\infty\to \mathcal{B}$ is not a projection. This fact can be emended via the…
Let $\mathcal{H}$ be a Hilbert space, and let $K(\mathcal{H})$ be the $C^*$-algebra of compact operators on $\mathcal{H}$. In this paper, we present some characterizations of the norm-parallelism for elements of a Hilbert…
Let $H_1,H_2$ be complex Hilbert spaces and $T$ be a densely defined closed linear operator (not necessarily bounded). It is proved that for each $\epsilon>0$, there exists a bounded operator $S$ with $\|S\|\leq \epsilon$ such that $T+S$ is…
This paper is a contribution to frame theory. Frames in a Hilbert space are generalizations of orthonormal bases. In particular, Gabor frames of $L^2(\mathbb{R})$, which are made of translations and modulations of one or more windows, are…
Let G be a simple Lie group of real rank one, and S the ideal boundary of the corresponding symmetric space of noncompact type (H^n_R, H^n_C, H^n_H or H^2_O). We show the finiteness of the possible values of the secondary characteristic…
We prove that the space of convex real projective structures on a surface of genus $g\ge 2$ admits a mapping class group invariant K\"ahler metric where Teichm\"uller space with Weil-Petersson metric is a totally geodesic complex…
A bi-unitary connection in subfactor theory of Jones producing a subfactor of finite depth gives a 4-tensor appearing in a recent work of Bultinck-Mariena-Williamson-Sahinoglu-Haegemana-Verstraete on 2-dimensional topological order and…
We fully characterize orthogonal projections of infinite right circular (round) cones in real Hilbert spaces. Another interpretation is that, given two vectors in a real Hilbert space, we establish the optimal estimate on the angle between…
The purpose of this note is to show that, if $\mcB$ is a uniformly convex Banach, then the dual space $\mcB'$ has a "Hilbert space representation" (defined in the paper), that makes $\mcB$ much closer to a Hilbert space then previously…
In this paper we consider the integral orthogonal group with respect to the quadratic form of signature $(2,3)$ given by $\left(\begin{smallmatrix} 0 & 1 \\ 1 & 0 \end{smallmatrix}\right) \perp \left(\begin{smallmatrix} 0 & 1 \\ 1 & 0…
Let $\beta>1$. Define a class of similitudes \[S=\left\{f_{i}(x)=\dfrac{x}{\beta^{n_i}}+a_i:n_i\in \mathbb{N}^{+}, a_i\in \mathbb{R}\right\}.\] Let $\mathcal{A}$ be the collection of all the self-similar sets generated by the similitudes…
The unitary group U(N) acts by conjugations on the space H(N) of NxN Hermitian matrices, and every orbit of this action carries a unique invariant probability measure called an orbital measure. Consider the projection of the space H(N) onto…
When a projection of a symmetric or Hermitian matrix to the positive semidefinite cone is computed approximately (or to working precision on a computer), a natural question is to quantify its accuracy. A straightforward bound invoking…
We characterize operators $T=PQ$ ($P,Q$ orthogonal projections in a Hilbert space $H$) which have a singular value decomposition. A spatial characterizations is given: this condition occurs if and only if there exist orthonormal bases…
For a given bounded positive (semidefinite) linear operator $A$ on a complex Hilbert space $\big(\mathcal{H}, \langle \cdot\mid \cdot\rangle \big)$, we consider the semi-Hilbertian space $\big(\mathcal{H}, \langle \cdot\mid \cdot\rangle_A…