Related papers: The von Neumann inequality for 3x3 matrices
A pattern of interpolation nodes on the disk is studied, for which the interpolation problem is theoretically unisolvent, and which renders a minimal numerical condition for the collocation matrix when the standard basis of Zernike…
In previous publications, we illustrated the effectiveness of the method of the inhomogeneous differential equation in calculating the electric polarizability in the one-dimensional problem. In this paper we extend our effort to apply the…
In this paper we consider permutations of sequences of partitions, obtaining a result which parallels von Neumann's theorem on permutations of dense sequences and uniformly distributed sequences of points.
Some inequalities for positive linear maps on matrix algebras are given, especially asymmetric extensions of Kadison's inequality and several operator versions of Chebyshev's inequality. We also discuss well-known results around the matrix…
We identify the Kontsevich-Penner matrix integral, for finite size $n$, with the isomonodromic tau function of a $3\times 3$ rational connection on the Riemann sphere with $n$ Fuchsian singularities placed in correspondence with the…
Let $p$ be a multilinear polynomial in several noncommuting variables, with coefficients in a algebraically closed field $K$ of arbitrary characteristic. In this paper we classify the possible images of $p$ evaluated on $3\times 3$…
We give an elementary proof of Sarason's solvability criterion for the Nevanlinna-Pick problem with boundary interpolation nodes and boundary target values. We also give a concrete parametrization of all solutions of such a problem. The…
Motivated by a recent result on finite-dimensional Hilbert spaces, we prove a Jensen's inequality for partial traces in semifinite von Neumann algebras. We also prove a similar inequality in the framework of general (non-tracial) von…
Recently Kosaki proved an uncertainty principle for matrices, related to Wigner-Yanase-Dyson information, and asked if a similar inequality could be proved in the von Neumann algebra setting. In this paper we prove such an uncertainty…
We solve a three point Nevanlinna-Pick problem in the Euclidean ball. In particular, we determine a class of rational functions that interpolate this problem.
A geometric inequality among three triangles, originating in circle packing problems, is introduced. In order to prove it, we reduce the original formulation to the nonnegativity of a particular polynomial in four real indeterminates.…
We define four 3x3 commuting contractions which do not dilate to commuting isometries. However they do satisfy the scalar von Neumann inequality. These matrices are all nilpotent of order 2. We also show that any three $3\times3$ commuting…
The problem of computing optimal orthogonal approximation to a given matrix has attracted growing interest in machine learning. Notable applications include the recent Muon optimizer or Riemannian optimization on the Stiefel manifold. Among…
We prove a sharp three sphere inequality for solutions to third order perturbations of a product of two second order elliptic operators with real coefficients. Then we derive various kinds of quantitative estimates of unique continuation…
Let X be a smooth projective minimal 3-fold of general type. We prove the sharp inequality K^3_X >= (2 /3)(2p_g(X) - 5), an analogue of the classical Noether inequality for algebraic surfaces of general type
In this paper we provide an application to the Neumann problem of a recent three critical points theorem.
We obtain necessary and sufficient conditions for Nevanlinna-Pick interpolation on the unit disk with the additional restriction that all analytic interpolating functions satisfy $f'(0)=0.$ Alternatively, these results can be interpreted as…
Nevanlinna-Pick interpolation developed from a topic in classical complex analysis to a useful tool for solving various problems in control theory and electrical engineering. Over the years many extensions of the original problem were…
We show how the known theory of noncommutative Orlicz spaces for semifinite von Neumann algebras equipped with an fns trace, may be recovered using crossed product techniques. Then using this as a template, we construct analogues of such…
Recent results of Davidson-Paulsen-Raghupathi-Singh give necessary and sufficient conditions for the existence of a solution to the Nevanlinna-Pick interpolation problem on the unit disk with the additional restriction that the interpolant…