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arXiv · 1504.05242

Criterion for $\mathbb{Z}_d$--symmetry of a Spectrum of a Compact Operator

Boris S. Mityagin
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Abstract

If $A$ is a compact operator in a Banach space and some power $A^q$ is nuclear we give a criterion of $\mathbb{Z}_{d}$ -- symmetry of its spectrum $\sigma{A}$ in terms of vanishing of the traces $\mathop{\mathit{Trace}} A^n$ for all $n$, $n \geq 0$, $n \neq 0 \mod d$, sufficiently large.

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Boris S. Mityagin. 2015-04-20. Criterion for $\mathbb{Z}_d$--symmetry of a Spectrum of a Compact Operator. https://arxiv.org/abs/1504.05242

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