论文标题
关于均质多项式和（对称）张量产物的强大亚分化性
On the strong subdifferentiability of the homogeneous polynomials and (symmetric) tensor products
论文作者
论文摘要
在本文中，我们研究了Banach空间规范$ \ Mathcal {p}（^n x，y^*）$，$ x \ hat {\ otimes}_π\ cdots \ cdots \ p.除其他结果外，我们表征了空间的规范$ \ MATHCAL {p}（^n \ ell_p，\ ell_ {q}），\ Mathcal {p}（^n l_ {m_1}，l_ {m_1}，l_ {m_2}}）$，and $ \ m nycal {p} p}可分辨的。还获得了多线性映射的类似结果。由于双重空间的强大尺寸差异性意味着反思性，因此我们在$ n $均质的多项式和$ n $ linear映射的空间的反射性方面提高了一些已知结果。关于投影（对称的）张量规范，我们在单位球体上的基本张量$ u $和$ u_s $的$ _s $ $ x \ hat {\ otimes}_π\ cdots \ hat {\ otimes} {\ otimes}_πx$ hat {具体而言，我们证明$ \ hat {\ outimes} _ {π_s，n} \ ell_2 $和$ \ ell_2 \ hat {\ otimes}_π\ cdots \ cdots \ chat \ hat {\ outimes}_π\ ell_2 $ y y $ subliperive ye $ subly in y $ co $ $ ud $ co $ c $ c $ c $ utife $ c \ hat {\ otimes} _ {π_s} c_0 $和$ c_0 \ hat {\ otimes}_πc_0$分别在$ u_s $和$ u $上分别是明显的，在复杂的情况下。
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.
