Some vector and operator generalized trapezoidal inequalities for continuous functions of selfadjoint operators in Hilbert spaces are given. Applications for power and logarithmic functions of operators are provided as well.

Distinguished selfadjoint extension of Dirac operators are constructed for a class of potentials including Coulombic ones up to the critical case, −|x|. The method uses Hardy-Dirac inequalities and quadratic form techniques.

For bounded linear operators A,B on a Hilbert space H we show the validity of the estimate ∑ λ∈σd(B) dist(λ,Num(A)) ≤ ‖B −A‖pSp , p ≥ 1, and apply it to recover and improve some Lieb-Thirring type inequalities for non-selfadjoint Jacobi and Schrödinger operators.

On utilizing the spectral representation of selfadjoint operators in Hilbert spaces, some approximations for the n-time di¤erentiable functions of selfadjoint operators in Hilbert spaces by two point Taylor’s type expansions are given. 1. Introduction Let U be a selfadjoint operator on the complex Hilbert space (H; h:; :i) with the spectrum Sp (U) included in the interval [m;M ] for some real n...

We prove Lieb-Thirring-type bounds on eigenvalues of non-selfadjoint Jacobi operators, which are nearly as strong as those proven previously for the case of selfadjoint operators by Hundertmark and Simon. We use a method based on determinants of operators and on complex function theory, extending and sharpening earlier work of Borichev, Golinskii and Kupin.

In this paper we introduce operator preinvex functions and establish a Hermite–Hadamard type inequality for such functions. We give an estimate of the right hand side of a Hermite–Hadamard type inequality in which some operator preinvex functions of selfadjoint operators in Hilbert spaces are involved. Also some Hermite–Hadamard type inequalities for the product of two operator preinvex functio...

We determine the possible nonzero eigenvalues of compact selfadjoint operators A, B(1), B(2), . . ., B(m) with the property that A = B(1) +B(2) +· · ·+B(m). When all these operators are positive, the eigenvalues were known to be subject to certain inequalities which extend Horn’s inequalities from the finite-dimensional case when m = 2. We find the proper extension of the Horn inequalities and ...