周期带状托普利兹算子的数值范围

IF 0.8 Q2 MATHEMATICS Advances in Operator Theory Pub Date : 2023-12-11 DOI:10.1007/s43036-023-00304-7

Benjamín A. Itzá-Ortiz, Rubén A. Martínez-Avendaño, Hiroshi Nakazato

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引用次数: 0

摘要

我们证明了一个（(n+1)\）周期性和（(2m+1)\）带状托普利茨算子的数值范围的闭包可以表示为某些符号矩阵的数值范围的不可数联盟的凸壳的闭包。与周期性三带（或三对角）情况相反，我们举例说明了一个二周期五带托普利兹算子，其数值范围的闭包不等于单个有限矩阵的数值范围。

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The numerical range of periodic banded Toeplitz operators

We prove that the closure of the numerical range of a \((n+1)\)-periodic and \((2m+1)\)-banded Toeplitz operator can be expressed as the closure of the convex hull of the uncountable union of numerical ranges of certain symbol matrices. In contrast to the periodic 3-banded (or tridiagonal) case, we show an example of a 2-periodic and 5-banded Toeplitz operator such that the closure of its numerical range is not equal to the numerical range of a single finite matrix.

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来源期刊

Advances in Operator Theory MATHEMATICS-

CiteScore

1.60

自引率

0.00%

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