论文标题
关于有界全体形态映射的组成理想和双重理想
On composition ideals and dual ideals of bounded holomorphic mappings
论文作者
论文摘要
通过J. Mujica应用线性化定理，我们研究了有限的全体形态映射的理想$ \ Mathcal {H}^\ infty \ circ \ Mathcal \ Mathcal {I} $，由操作员构成生成的{I} $。引入了$ \ mathcal {i} $的有界三晶双重理想，其元素的特征是那些通过$ \ mathcal {i}^\ mathrm {dual} $进行分解的元素。对于复杂的Banach Spaces $ E $和$ f $，我们还分析了从开放子集$ u \ subseteq e $到$ f $的新的界面式全体形状映射的新理想，例如$ p $ p $ integral holomorphic映射和$ p $ p $ - 努力 - 努力 - 努力 - 努力 - 努力 - 努力 - 努力 - 努力的holomorphic映射，$ 1 \ 1 \ leq p <\ leq p <\ fle f <\ fly f <\ fefty $。我们证明，每个$ p $ integral（$ p $ - 核）的全态映射从$ u $到$ f $具有相对较弱的紧凑型（紧凑）范围。
Applying a linearization theorem due to J. Mujica, we study the ideals of bounded holomorphic mappings $\mathcal{H}^\infty\circ\mathcal{I}$ generated by composition with an operator ideal $\mathcal{I}$. The bounded-holomorphic dual ideal of $\mathcal{I}$ is introduced and its elements are characterized as those that admit a factorization through $\mathcal{I}^\mathrm{dual}$. For complex Banach spaces $E$ and $F$, we also analyze new ideals of bounded holomorphic mappings from an open subset $U\subseteq E$ to $F$ such as $p$-integral holomorphic mappings and $p$-nuclear holomorphic mappings with $1\leq p<\infty$. We prove that every $p$-integral ($p$-nuclear) holomorphic mapping from $U$ to $F$ has relatively weakly compact (compact) range.
