Spectrality of the product does not imply that the components are spectral
Abstract
Greenfeld and Lev [J. Anal. Math., 16 (2020), 409–441] conjectured that the Cartesian product of two sets A A and B B is spectral if and only if A A and B B are spectral. We construct a counterexample to this conjecture using the existence of a tile that has no spectra.
Fields of Study & Subjects
Advanced Banach Space Theory
Mathematical Analysis and Transform Methods
Holomorphic and Operator Theory
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Volume
- 154
- Issue
- 3
- Pages
- 1073–1076
- Publication date
- 15 January 2026
- Language
- EN