On the spectrum of the symmetric tensor products of certain Hilbert-space operators

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发表日期：

2026年3月14日

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Yuchi Yang,
Yuanhang Zhang

摘要

This paper primarily investigates the spectral properties of symmetric tensor products of Hilbert-space operators. For a unilateral weighted shift operator $S_w$ $S_{w}$ , we present an algorithm to compute the point spectrum of its symmetric and antisymmetric tensor products with the adjoint $S_w^*$ $S_{w}^{*}$ . Additionally, we analyze the symmetric tensor product of an injective unilateral weighted shift $S_\alpha $ $S_{α}$ and a diagonal operator M on $l^2$ $l^{2}$ , demonstrating that its point spectrum must be contained in $\{0\}$ ${0}$ .