Protecting points from operator pencils
Albrecht Seelmann, Matthias T\"aufer, Kre\v{s}imir Veseli\'c

TL;DR
This paper classifies the spectral sets formed by the union of spectra of self-adjoint operator pencils, showing they are complements of at most countable discrete subsets of the real line.
Contribution
It provides a complete classification of spectral sets generated by operator pencils with bounded, non-negative, non-zero operators, identifying them as complements of discrete subsets of the real line.
Findings
Spectral sets are exactly the complements of discrete subsets of .
These sets contain no accumulation points.
The classification applies to all such operator pencils.
Abstract
We classify all sets of the form where and are self-adjoint operators and is bounded, non-negative, and non-zero. We show that these sets are exactly the complements of discrete subsets of , that is, of at most countable subsets of that contain none of their accumulation points.
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