Related papers: The projection constant for the trace class

Given a finite collection $\mathbf{V}:=(V_1,\dots,V_N)$ of closed linear subspaces of a real Hilbert space $H$, let $P_i$ denote the orthogonal projection operator onto $V_i$ and $P_{i,\lambda}:= (1-\lambda)I + \lambda P_i$ denote its…

We prove a unified trace-average formula for the $k$-th higher trace $\lambda_k(A)=\operatorname{tr}(\Lambda^k A)$ of a linear operator $A$ on a finite-dimensional normed space. The formula averages the matrix coefficient…

Using free random varaibles we find an embedding of the operator space $OH$ in the predual of a von Neumann algebra. The properties of this embedding allow us to determined the projection constant of $OH_n$, i.e. there exists a projection…

For the Bergman projection operator $P$ we prove that $ \|P\|_{{L^1(B,d\lambda)\rightarrow B_1}}= \frac {(2n+1)!}{n!}.$ Here $\lambda$ stands for the invariant metric in the unit ball $B$ of $\mathbf{C}^n$, and $B_1$ denotes the Besov space…

We present several operator and norm inequalities for Hilbert space operators. In particular, we prove that if $A_{1},A_{2},...,A_{n}\in {\mathbb B}({\mathscr H})$, then…

We present a proof that the operator norm of the commutator of certain spectral projections associated with spin operators converges to $\frac 1 2$ in the semiclassical limit. The ranges of the projections are spanned by all eigenvectors…

We study integral operators on the space of square-integrable functions from a compact set, $X$, to a separable Hilbert space, $H$. The kernel of such an operator takes values in the ideal of Hilbert-Schmidt operators on $H$. We establish…

We present other examples illustrating the operator-theoretic approach to invariant integrals on quantum homogeneous spaces developed by Kuersten and the second author. The quantum spaces are chosen such that their coordinate algebras do…

Let $C_1(H)$ denote the space of all trace class operators on an arbitrary complex Hilbert space $H$. We prove that $C_1(H)$ satisfies the $\lambda$-property, and we determine the form of the $\lambda$-function of Aron and Lohman on the…

We investigate projection constants within classes of multivariate polynomials over finite-dimensional real Hilbert spaces. Specifically, we consider the projection constant for spaces of spherical harmonics and spaces of homogeneous…

The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is…

We develop a principal trace and generalized index formula for a Dirac-Schr\"odinger operator $D$ on open space of odd dimension $d\geq 3$ with a potential given by a family of self-adjoint unbounded operators acting on a infinite…

Given a frequency sequence $\omega=(\omega_n)$ and a finite subset $J \subset \mathbb{N}$, we study the space $\mathcal{H}_{\infty}^{J}(\omega)$ of all Dirichlet polynomials $D(s) := \sum_{n \in J} a_n e^{-\omega_n s}, \, s \in \mathbb{C}$.…

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…

In general, it is a non trivial task to determine the adjoint $S^*$ of an unbounded operator $S$ acting between two Hilbert spaces. We provide necessary and sufficient conditions for a given operator $T$ to be identical with $S^*$. In our…

This article - a part of a multipaper project investigating arithmetic mean ideals - investigates the codimension of commutator spaces [I, B(H)] of operator ideals on a separable Hilbert space, i.e., ``How many traces can an ideal support?"…

We use Voiculescu's concept of free probability to construct a completely isomorphic embedding of the operator space OH in the predual of a von Neumann algebra. We analyze the properties of this embedding and determine the operator space…

A natural generalization of Krein's theorem to a pair of commuting tuples $\left(H_1^0,H_2^0\right)$ and $\left(H_1,H_2\right)$ of bounded self-adjoint operators in a separable Hilbert space $\mathcal{H}$ with $H_j-H_j^0 = V_j\in…

A Hilbert space operator $S\in\B$ is $n$-quasi left $m$-invertible (resp., left $m$-invertible) by $T\in\B$, $m,n \geq 1$ some integers, if $S^{*n}p(S,T)S^n=0$ (resp., $p(S,T)=0$), where…

Naively the Hilbert space of a sigma model has to be defined as an L^2 space of functions on the space of free loops of the target. This object is not well defined. In this note we study a finite-dimensional approximations L_N(S^n) of the…