We study refinements between spectral resolutions in an arbitrary II1 factor M and obtain diffuse (maximal) refinements of spectral resolutions. We construct models of operators with respect to diffuse spectral resolutions. ...

In this work we present Lyapunov type inequalities for generalized one dimensional Laplacian operators defined by positive atomless Borel measures. As applications, we present lower bounds for the first eigenvalue when the ...

Let A be a C*-algebra and φ{symbol} : A → L (H) be a positive unital map. Then, for a convex function f : I → R defined on some open interval and a self-adjoint element a ∈ A whose spectrum lies in I, we obtain a Jensen's-type ...

Let A be an n×n complex Hermitian matrix and let λ(A)=(λ1,…,λn)∈Rn denote the eigenvalues of A, counting multiplicities and arranged in non-increasing order. Motivated by problems arising in the theory of low rank matrix ...

The construction of (asymptotic) simultaneous confidence bands for some time series problems is studied, typically for the sample autocorrelogram and windowed spectral density estimate. The following approaches are explored: ...

This paper is devoted to various considerations on a family of sharp interpolation inequalities on the sphere, which in dimension greater than 1 interpolate between Poincar´e, logarithmic Sobolev and critical Sobolev ...

Introduction ​The eigenvalue problems for quasilinear and nonlinear operators present many differences with the linear case, and a Lyapunov inequality for quasilinear resonant systems showed the existence of eigenvalue ...