论文标题
Cohen在Banach空间上强烈p-summ thummormorthic映射
Cohen strongly p-summing holomorphic mappings on Banach spaces
论文作者
论文摘要
令$ e $和$ f $为复杂的Banach空间，$ u $是$ e $的开放子集，$ 1 \ leq p \ leq \ leq \ infty $。我们介绍并研究了Cohen的概念强烈的$ p $ - 周到的全态映射从$ u $到$ f $，这是一个强烈的$ p $ p $ summ-summ-umm-summing线性操作员的holomorphic版本。对于这样的映射，我们同时建立了Pietsch的统治/分解理论，并通过$ \ Mathcal {g}^\ infty（u）$（$ \ Mathcal {h}^\ infty（u）$）及其对$ \ nathcal $ \ nathcal $ \ fift $ \ fiftty（unfty）分析了它们的线性化。有关空间$ \ nathcal {d} _p^{\ Mathcal {h}^\ infty}（u，f）$由这种映射形成并具有自然规范$ d_p^{\ Mathcal {\ Mathcal {h}^\ infty} $，我们表明了它是常规的banach banach banach Indort younder nounder的组合，并构成了杂物的组合。 $ p $ - 点线性操作员。此外，我们确定空间$（\ MATHCAL {d} _p^{\ MATHCAL {H}^\ infty}（u，f^*），d_p^{\ Mathcal {h}^\ intcal {使用雪佛兰 - saphar norm $ g_p $。
Let $E$ and $F$ be complex Banach spaces, $U$ be an open subset of $E$ and $1\leq p\leq\infty$. We introduce and study the notion of a Cohen strongly $p$-summing holomorphic mapping from $U$ to $F$, a holomorphic version of a strongly $p$-summing linear operator. For such mappings, we establish both Pietsch domination/factorization theorems and analyse their linearizations from $\mathcal{G}^\infty(U)$ (the canonical predual of $\mathcal{H}^\infty(U)$) and their transpositions on $\mathcal{H}^\infty(U)$. Concerning the space $\mathcal{D}_p^{\mathcal{H}^\infty}(U,F)$ formed by such mappings and endowed with a natural norm $d_p^{\mathcal{H}^\infty}$, we show that it is a regular Banach ideal of bounded holomorphic mappings generated by composition with the ideal of strongly $p$-summing linear operators. Moreover, we identify the space $(\mathcal{D}_p^{\mathcal{H}^\infty}(U,F^*),d_p^{\mathcal{H}^\infty})$ with the dual of the completion of tensor product space $\mathcal{G}^\infty(U)\otimes F$ endowed with the Chevet--Saphar norm $g_p$.
