关于齐次多项式和（对称）张量积的强次可微性
On the strong subdifferentiability of the homogeneous polynomials and (symmetric) tensor products
摘要：
本文研究了Banach空间$\mathcal{P}(^N X, Y^*)$，$X \hat{\otimes}_π\cdots \hat{\otimes}_πX$和$\hat{\otimes}_{π_s,N} X$的范数的（一致）强次可微性.在其他结果中，我们刻画了空间$\mathcal{P}(^N \ell_p, \ell_{q}), \mathcal{P}(^N l_{M_1}, l_{M_2})$和$\mathcal{P}(^N d(w,p), l_{M_2})$的范数是强次可微的。对于多重线性映射也得到了类似的结果。由于对偶空间的强次可微性蕴涵着自反性，本文改进了有关$N$ -齐次多项式空间和$N$ -线性映射空间的自反性的一些已知结果.关于射影（对称）张量范数，我们提供了积极的结果的子集$U$和$U_s$的基本张量的单位球面上的$X \hat{\otimes}_π\cdots \hat{\otimes}_πX$和$\hat{\otimes}_{π_s,N} X$，分别。具体地说，我们证明了$\hat{\otimes}_{π_s,N} \ell_2$和$\ell_2 \hat{\otimes}_π\cdots \hat{\otimes}_π\ell_2$是一致强次可微的$U_s$和$U$，分别，和$c_0 \hat{\otimes}_{π_s} c_0$和$c_0 \hat{\otimes}_πc_0$是强次可微的$U_s$和$U$，分别在复杂的情况下。
英文摘要：
In this paper, we study the (uniform) strong subdifferentiability of the norms of the Banach spaces $\mathcal{P}(^N X, Y^*)$, $X \hat{\otimes}_π\cdots \hat{\otimes}_πX$ and $\hat{\otimes}_{π_s,N} X$. Among other results, we characterize when the norms of the spaces $\mathcal{P}(^N \ell_p, \ell_{q}), \mathcal{P}(^N l_{M_1}, l_{M_2})$, and $\mathcal{P}(^N d(w,p), l_{M_2})$ are strongly subdifferentiable. Analogous results for multilinear mappings are also obtained. Since strong subdifferentiability of a dual space implies reflexivity, we improve some known results on the reflexivity of spaces of $N$-homogeneous polynomials and $N$-linear mappings. Concerning the projective (symmetric) tensor norms, we provide positive results on the subsets $U$ and $U_s$ of elementary tensors on the unit spheres of $X \hat{\otimes}_π\cdots \hat{\otimes}_πX$ and $\hat{\otimes}_{π_s,N} X$, respectively. Specifically, we prove that $\hat{\otimes}_{π_s,N} \ell_2$ and $\ell_2 \hat{\otimes}_π\cdots \hat{\otimes}_π\ell_2$ are uniformly strongly subdifferentiable on $U_s$ and $U$, respectively, and that $c_0 \hat{\otimes}_{π_s} c_0$ and $c_0 \hat{\otimes}_πc_0$ are strongly subdifferentiable on $U_s$ and $U$, respectively, in the complex case.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
