Spectrally Simple Spectra without Irreducible Nonnegative Realizations

We give a counterexample to a conjecture of Johnson, Marijuán, and Pisonero: we show that the spectrum {1, 1/2, ±i/√3} is realizable and spectrally simple, but has no irreducible nonnegative realization. More generally, we prove their nonexistence conjecture for an order-four boundary family.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-09
DOI
https://doi.org/10.5281/zenodo.23263430
Primary Topic
Holomorphic and Operator Theory
Type
preprint
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preprint

Spectrally Simple Spectra without Irreducible Nonnegative Realizations

Yair Lavi
Zenodo (CERN European Organization for Nuclear Research)
Holomorphic and Operator Theory
preprint

Spectrally Simple Spectra without Irreducible Nonnegative Realizations

Yair Lavi
preprint en

Abstract

We give a counterexample to a conjecture of Johnson, Marijuán, and Pisonero: we show that the spectrum {1, 1/2, ±i/√3} is realizable and spectrally simple, but has no irreducible nonnegative realization. More generally, we prove their nonexistence conjecture for an order-four boundary family.

Zenodo (CERN European Organization for Nuclear Research)
Holomorphic and Operator Theory
DOIOpen Access PDFOpenAlex
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Spectrally Simple Spectra without Irreducible Nonnegative Realizations — Yair Lavi · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS