Related papers: The projection constant for the trace class

We introduce new entanglement measures on the set of density operators on tensor product Hilbert spaces. These measures are based on the greatest cross norm on the tensor product of the sets of trace class operators on Hilbert space. We…

A certain subspace of the Hilbert space of square-integrable functions on the unit interval has been considered by Nyman, Beurling, and others, with the result that the constant function 1 belongs to it if and only if the Riemann Hypothesis…

The aim of this article is to explore in all remaining aspects the spectral theory of locally normal operators. In a previous article we proved the spectral theorem in terms of locally spectral measures. Here we prove the spectral theorem…

We investigate projection constants for spaces of bihomogeneous harmonic and bihomogeneous polynomials on the unit sphere in finite-dimensional complex Hilbert spaces. Using averaging techniques, we demonstrate that the minimal norm…

Paszkiewicz's conjecture asserts that given a decreasing sequence $T_1\ge T_2\ge \dots$ of positive contractions on a separable infinite-dimensional Hilbert space $H$, the product $S_n=T_nT_{n-1}\cdots T_1$ converges in the strong operator…

Given $N\ge2$ closed subspaces $M_1,\dotsc, M_N$ of a Hilbert space $X$, let $P_k$ denote the orthogonal projection onto $M_k$, $1\le k\le N$. It is known that the sequence $(x_n)$, defined recursively by $x_0=x$ and $x_{n+1}=P_N\cdots…

In this article, we prove the following spectral theorem for right linear normal operators (need not to be bounded) in quaternionic Hilbert spaces: Let $T$ be an unbounded right quaternionic linear normal operator in a quaternionic Hilbert…

The paper is concerned with the problem of identifying the norm attaining operators in the von Neumann algebra generated by two orthogonal projections on a Hilbert space. This algebra contains every skew projection on that Hilbert space and…

We consider an abstract sequence $\{A_n\}_{n=1}^\infty$ of closed symmetric operators on a separable Hilbert space $\mathcal{H}$. It is assumed that all $A_n$'s have equal deficiency indices $(k,k)$ and thus self-adjoint extensions…

A fundamental inequality for Hilbert spaces is the $\ell_1-\ell_2$-norm inequality which gives that for any $x \in H^n$, $\|x\|_1\le \sqrt{n}\|x\|_2.$ But this is a strict inequality for all but vectors with constant modulus for their…

In the first section we provide a solution to the M. G. Krein problem about an inner description of the space $L_2(\Sigma,H).$ In the second section we introduce the multiplicity function for an operator measure. Making use of the…

We establish higher order trace formulas for pairs of contractions along a multiplicative path generated by a self-adjoint operator in a Schatten-von Neumann ideal, removing earlier stringent restrictions on the kernel and defect operator…

Recently the authors solved a long-standing problem and showed that for an arbitrary pair of contractions on Hilbert space with trace class difference has an integrable spectral shift function on the unit circle ${\Bbb T}$ and an analogue…

We present a streamlined approach for generalized strong and norm convergence of self-adjoint operators in different Hilbert spaces. In particular, we establish convergence of associated (semi-)groups, (essential) spectra and spectral…

We establish that trace inequalities $$\|D^{k-1}u\|_{L^{\frac{n-s}{n-1}}(\mathbb{R}^{n},d\mu)} \leq c \|\mu\|_{L^{1,n-s}(\mathbb{R}^{n})}^{\frac{n-1}{n-s}}\|\mathbb{A}[D]u\|_{L^{1}(\mathbb{R}^{n},d\mathscr{L}^{n})}$$ hold for vector fields…

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…

The long-standing problem of minimal projections is addressed from a computational point of view. Techniques to determine bounds on the projection constants of univariate polynomial spaces are presented. The upper bound, produced by a…

This paper gives a self-contained introduction to the Hilbert projective metric $\mathcal{H}$ and its fundamental properties, with a particular focus on the space of probability measures. We start by defining the Hilbert pseudo-metric on…

Spectral properties of bounded linear operators play a crucial role in several areas of mathematics and physics. For each self-adjoint, trace-class operator $O$ we define a set $\Lambda_n\subset \mathbb{R}$, and we show that it converges to…

We present a concentration result concerning random weighted projections in high dimensional spaces. As applications, we prove (1) New concentration inequalities for random quadratic forms; (2) The infinity norm of most unit eigenvectors of…