General preservers of quasi-commutativity on self-adjoint operators

Commutativity, Comonotonicity, and Choquet Integration of Self-adjoint Operators∗

In this work we propose a definition of comonotonicity for elements ofB (H)sa, i.e., bounded self-adjoint operators defined over a complex Hilbert space H. We show that this notion of comonotonicity coincides with a form of commutativity. Intuitively, comonotonicity is to commutativity as monotonicity is to bounded variation. We also define a notion of Choquet expectation for elements of B (H)s...

On Families of Self Adjoint Operators

Adjoint and self - adjoint differential operators on graphs ∗

A differential operator on a directed graph with weighted edges is characterized as a system of ordinary differential operators. A class of local operators is introduced to clarify which operators should be considered as defined on the graph. When the edge lengths have a positive lower bound, all local self-adjoint extensions of the minimal symmetric operator may be classified by boundary condi...

Diagonals of Self-adjoint Operators

The eigenvalues of a self-adjoint n×n matrix A can be put into a decreasing sequence λ = (λ1, . . . , λn), with repetitions according to multiplicity, and the diagonal of A is a point of R that bears some relation to λ. The Schur-Horn theorem characterizes that relation in terms of a system of linear inequalities. We prove an extension of the latter result for positive trace-class operators on ...

Self-adjoint operators on surfaces in Rn

Our aim in this paper is to define principal and characteristic directions at points on a smooth 2-dimensional surface in the Euclidean space R in such a way that their equations together with that of the asymptotic directions behave in the same way as the triple formed by their counterpart on smooth surfaces in the Euclidean space R. The definitions we propose are derived from a more general a...