Diagonals of self-adjoint operators II: non-compact operators
Document Type
Article
Publication Date
6-23-2024
Abstract
Given a self-adjoint operator T on a separable infinite-dimensional Hilbert space we study the problem of characterizing the set D(T) of all possible diagonals of T. For operators T with at least two points in their essential spectrum σess(T), we give a complete characterization of D(T) for the class of self-adjoint operators sharing the same spectral measure as T with a possible exception of multiplicities of eigenvalues at the extreme points of σess(T). We also give a more precise description of D(T) for a fixed self-adjoint operator T, albeit modulo the kernel problem for special classes of operators. These classes consist of operators T for which an extreme point of the essential spectrum σess(T) is also an extreme point of the spectrum σ(T). Our results generalize a characterization of diagonals of orthogonal projections by Kadison, Blaschke-type results of Müller and Tomilov, and Loreaux and Weiss, and a characterization of diagonals of operators with finite spectrum by the authors.
DOI
Version of Record: 10.1007/s00208-024-02910-z ; arXiv: 2304.14468
Source Publication
Mathematische Annalen
Recommended Citation
Version of record:
Bownik, M., & Jasper, J. (2024). Diagonals of self-adjoint operators II: non-compact operators. Mathematische Annalen. https://doi.org/10.1007/s00208-024-02910-z
arXiv repository preprint:
arXiv:2304.14468 [math.FA]
Comments
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The published article appears in the journal Mathematische Annalen, published by SpringerNature, and is available by subscription. It was published online in June 2024 ahead of inclusion in an issue.