标题： 关于某些希尔伯特空间算子对称张量积的谱 显示英文标题

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

摘要： 本文主要研究希尔伯特空间算子对称张量积的谱性质。 对于一个单边加权移位算子$S_w$，我们提出一种算法来计算其与共轭算子$S_w^*$的对称和反对称张量积的点谱。 此外，我们分析了一个单边加权移位算子$S_\alpha$与一个对角算子$M$在$l^2$上的对称张量积，证明其点谱必须包含在$\{0\}$中。 显示英文摘要

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