Triple variational principles for self-adjoint operator functions

Langer, Matthias and Strauss, Michael (2016) Triple variational principles for self-adjoint operator functions. Journal of Functional Analysis, 270 (6). pp. 2019-2047. ISSN 0022-1236

[img]
Preview
Text (Langer-Strauss-JFA2016-triple-variational-principles-for-self-adjoint-operator-functions)
Langer_Strauss_JFA2016_triple_variational_principles_for_self_adjoint_operator_functions.pdf
Final Published Version
License: Creative Commons Attribution 4.0 logo

Download (540kB)| Preview

    Abstract

    For a very general class of unbounded self-adjoint operator function we prove upper bounds for eigenvalues which lie within arbitrary gaps of the essential spectrum. These upper bounds are given by triple variations. Furthermore, we find conditions which imply that a point is in the resolvent set. For norm resolvent continuous operator functions we show that the variational inequality becomes an equality.