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arXiv 2310.063312023-10math.FA

酉算子曲线谱界的几何

Geometry of spectral bounds of curves of unitary operators

Martin Miglioli

备注：: 10 pages, minor corrections where made to the first version

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AI总结：

研究利用酉算子群及其作用球面上的度量几何方法，重新证明酉算子乘积的谱界定理，并将其推广至可微曲线。

摘要：

本文给出了关于酉算子乘积谱界的一个定理的新证明，并将该定理推广到可微曲线情形。证明过程运用了酉算子群以及这些算子所作用的球面上的度量几何论证。

英文摘要：

This article presents a new proof of a theorem concerning bounds of the spectrum of the product of unitary operators and a generalization for differentiable curves of this theorem. The proofs involve metric geometric arguments in the group of unitary operators and the sphere where these operators act.

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