A new construction for the form sum of positive, selfadjoint operators is given in this paper. The situation is a bit more general, because our aim is to add positive, symmetric operators. With the help of the used method, some commutation properties of the form sum extension are observed.

We continue the spectral analysis of differential operators with complex coefficients, extending some results for Sturm-Liouville to higher order operators. give conditions essential spectrum be empty, and operator have compact resolvent. Conditions are given on coefficients resolvent Hilbert-Schmidt. These new even real i.e., selfadjoint case. Asymptotic is a central tool. See also https://ejd...

We present recent progress in the understanding of the spectral and subelliptic properties of non-elliptic quadratic operators with application to the study of return to equilibrium for some systems of chains of oscillators. We then explain how these results allow to describe the spectral properties and to give sharp resolvent estimates for some classes of non-selfadjoint pseudodi erential oper...

In 2005, Shen introduced a new invariant, G(N), of a di use von Neumann algebra N with a xed faithful trace, and he used this invariant to give a uni ed approach to showing that large classes of II1 factors M are singly generated. This paper focuses on properties of this invariant. We relate G(M) to the number of self-adjoint generators of a II1 factor M : if G(M) < n/2, then M is generated by ...

We introduce and study the variational problem to maximize the determinant of a random selfadjoint operators obtained from discrete abelian or nonabelian lattice gauge fields. We prove the existence of minima and give rough estimates of the functional for multi-particle operators.

The multivariate orthogonal polynomials are related to a family of commuting selfadjoint operators. The spectral theorem for these operators is used to prove that a polynomial sequence satisfying a vector-matrix form of the three-term relation is orthonormal with a determinate measure.