论文标题
在相对$ p $ compact范围内的全态映射上
On holomorphic mappings with relatively $p$-compact range
论文作者
论文摘要
Related to the concept of $p$-compact operator with $p\in [1,\infty]$ introduced by Sinha and Karn, this paper deals with the space $\mathcal{H}^\infty_{\mathcal{K}_p}(U,F)$ of all Banach-valued holomorphic mappings on an open subset $U$ of a complex Banach space $ e $的范围相对$ p $ compact子集为$ f $。我们表征了这样的全态映射，就像那些在$ \ Mathcal {h}^\ infty（u）$的$ \ Mathcal（h}^\ infty（u）$是$ p $ -compact Operators的规范上的线性化的映射。这个事实使我们能够对它们进行完整的研究。 We show that $\mathcal{H}^\infty_{\mathcal{K}_p}$ is a surjective Banach ideal of bounded holomorphic mappings which is generated by composition with the ideal of $p$-compact operators and contains the Banach ideal of all right $p$-nuclear holomorphic mappings.我们还以相对$ p $ -compact的范围为特征，将其作为有界的全态映射，通过$ \ ell_ {p^*} $的商分解，或者将转poses的转换为quasi $ p $ p $ -nuclear ocerators（分别分别通过$ el el el el el el el el el el el el e el el e el el \ ell of Ell-el-p $ -nuc-n核操作员）。
Related to the concept of $p$-compact operator with $p\in [1,\infty]$ introduced by Sinha and Karn, this paper deals with the space $\mathcal{H}^\infty_{\mathcal{K}_p}(U,F)$ of all Banach-valued holomorphic mappings on an open subset $U$ of a complex Banach space $E$ whose ranges are relatively $p$-compact subsets of $F$. We characterize such holomorphic mappings as those whose Mujica's linearisations on the canonical predual of $\mathcal{H}^\infty(U)$ are $p$-compact operators. This fact allows us to make a complete study of them. We show that $\mathcal{H}^\infty_{\mathcal{K}_p}$ is a surjective Banach ideal of bounded holomorphic mappings which is generated by composition with the ideal of $p$-compact operators and contains the Banach ideal of all right $p$-nuclear holomorphic mappings. We also characterize holomorphic mappings with relatively $p$-compact ranges as those bounded holomorphic mappings which factorize through a quotient space of $\ell_{p^*}$ or as those whose transposes are quasi $p$-nuclear operators (respectively, factor through a closed subspace of $\ell_p$).
