标题： 对加权移位算子的对称和反对称张量积的范数 显示英文标题

标题： The norms for symmetric and antisymmetric tensor products of the weighted shift operators

摘要： 在本文中，我们研究加权移位算子对称和反对称张量积的范数。 通过证明对于$n\geq 2$，$$\|S_{\alpha}^{l_1}\odot\cdots \odot S_{\alpha}^{l_k}\odot S_{\alpha}^{*l_{k+1}}\odot\cdots \odot S_{\alpha}^{*l_{n}}\| =\mathop{\prod}_{i=1}^n\left \| S_{\alpha}^{{l_{i}}}\right\|, \text{ for any} \ (l_1,l_2\cdots l_n)\in\mathbb N^n$$当且仅当权满足正则性条件，我们部分解决了\cite[Problem 6 and Problem 7]{GA}。 可以看出，函数空间上的大多数加权移位算子，包括加权Bergman移位、Hardy移位、Dirichlet移位等，都满足正则性条件。 此外，在论文最后，我们解决了\cite[Problem 1 and Problem 2]{GA}。 显示英文摘要

摘要： In the present paper, we study the norms for symmetric and antisymmetric tensor products of weighted shift operators. By proving that for $n\geq 2$, $$\|S_{\alpha}^{l_1}\odot\cdots \odot S_{\alpha}^{l_k}\odot S_{\alpha}^{*l_{k+1}}\odot\cdots \odot S_{\alpha}^{*l_{n}}\| =\mathop{\prod}_{i=1}^n\left \| S_{\alpha}^{{l_{i}}}\right\|, \text{ for any} \ (l_1,l_2\cdots l_n)\in\mathbb N^n$$ if and only if the weight satisfies the regularity condition, we partially solve \cite[Problem 6 and Problem 7]{GA}. It will be seen that most weighted shift operators on function spaces, including weighted Bergman shift, Hardy shift, Dirichlet shift, etc, satisfy the regularity condition. Moreover, at the end of the paper, we solve \cite[Problem 1 and Problem 2]{GA}.