Related papers: Projecting onto Helson matrices in Schatten classe…

Let $X$ be a finite-dimensional normed space and let $Y \subseteq X$ be its proper linear subspace. The set of all minimal projections from $X$ to $Y$ is a convex subset of the space all linear operators from $X$ to $X$ and we can consider…

We establish Marstrand-type as well as Besicovich-Federer-type projection theorems for closest-point projections onto hyperplanes in the normed space $\mathbb{R}^{n}$. In particular, we prove that if a norm on $\mathbb{R}^{n}$ is…

For the L_2-orthogonal projector P onto spaces of linear splines over simplicial partitions of polyhedral domains in R^d, d>1, we show that the L_infty norm of P cannot be bounded uniformly with respect to the partition. This is in contrast…

We use the principle of almost orthogonality to give a new and simple proof that a sparse Lerner operator is bounded on a matrix- or operator-weighted space $L_W^{2}(\mu)$, where $\mu$ is a doubling measure on $\R^d$ if and only if the…

Motivated by Barr{\'\i}a-Halmos's \cite[Question 19]{barria1982asymptotic} and Halmos's \cite[Problem 237]{Halmos1978A}, we explore projections in Toeplitz algebra on the Hardy space. We show that the product of two Toeplitz (Hankel)…

We generalize some aspects of the theory of compact projections relative to a C*-algebra, to the setting of more general algebras. Our main result is that compact projections are the decreasing limits of `peak projections', and in the…

We prove endpoint and sparse-like bounds for Bergman projectors on nonhomogeneous, radial trees $X$ that model manifolds with possibly unbounded geometry. The natural Bergman measures on $X$ may fail to be doubling, and even locally…

We show that the Nichols algebra of a simple Yetter-Drinfeld module over a projective special linear group over a finite field whose support is a semisimple orbit has infinite dimension, provided that the elements of the orbit are…

This paper develops nonasymptotic growth and concentration bounds for a product of independent random matrices. These results sharpen and generalize recent work of Henriksen-Ward, and they are similar in spirit to the results of…

We show that $L^\infty$-norms of orthoprojectors on certain types of perturbations of spline spaces are bounded independently of the knot sequence. Explicit applications of this result are given, one of them being orthoprojectors onto…

We show that under natural and quite general assumptions, a large part of a matrix for a bounded linear operator on a Hilbert space can be preassigned. The result is obtained in a more general setting of operator tuples leading to…

Let $0<p,q\leq \infty$ and denote by $\mathcal S_p^N$ and $\mathcal S_q^N$ the corresponding Schatten classes of real $N\times N$ matrices. We study approximation quantities of natural identities $\mathcal S_p^N\hookrightarrow \mathcal…

According to the von Neumann-Halperin and Lapidus theorems, in a Hilbert space the iterates of products or, respectively, of convex combinations of orthoprojections are strongly convergent. We extend these results to the iterates of convex…

Let $\mathbb{B}(\mathcal{H})$ be the algebra of all bounded linear operators on a Hilbert space $\mathcal{H}$ and let $N(\cdot)$ be a norm on $\mathbb{B}(\mathcal{H})$. For every $0\leq \nu \leq 1$, we introduce the $w_{_{(N,\nu)}}(A)$ as…

We dominate non-integral singular operators by adapted sparse operators and derive optimal norm estimates in weighted spaces. Our assumptions on the operators are minimal and our result applies to an array of situations, whose prototype are…

Let $X,Y$ be Banach spaces, and fix a linear operator $T \in \mathcal{L}(X,Y)$, and ideals $\mathcal{I}, \mathcal{J}$ on $\omega$. We obtain Silverman--Toeplitz type theorems on matrices $A=(A_{n,k}: n,k \in \omega)$ of linear operators in…

We study the projection constant of the space of operators on $n$-dimensional Hilbert spaces, with the trace norm, $\mathcal S_1(n)$. We show an integral formula for the projection constant of $\mathcal S_1(n)$; namely $…

Boundedness for a class of projection operators, which includes the coordinate projections, on matrix weighted $L^p$-spaces is completely characterised in terms of simple scalar conditions. Using the projection result, sufficient…

We prove that the set of orthogonal projections on a Hilbert space equipped with the length metric is $\frac\pi2$-geodesic. As an application, we consider the problem of variation of spectral subspaces for bounded linear self-adjoint…

In any infinite dimensional Hilbert space $\mathcal H$ there exist orthogonal projections $Q_1$, $Q_2$ and $Q_3$, such that a sequence $(P_n... P_1(x))$ diverges in norm for some $P_1,P_2,...\in\{Q_1,Q_2,Q_3\}$ and $x\in\mathcal H$.