Factorization of weakly continuous holomorphic mappings

阿戴尔环群与完美oid类比：阿戴尔射影线上的因式分解与全纯丛

Adelic Loop Groups and Perfectoid Analogies: Factorization and Holomorphic Bundles on the Adelic Projective Line

研究在通用一维螺线管上的阿戴尔环群理论，引入阿戴尔射影线等，建立多个定理得出猜想，发展相关几何并与完美oid几何比较，得到猜想的重新表述，核心方法是构建理论体系并进行比较，主要贡献是丰富了相关理论及得出新猜想表述。

Factorization of completely bounded maps through reflexive operator spaces with applications to weak almost periodicity

Let $(M,Γ)$ be a Hopf--von Neumann algebra, so that $M_\ast$ is a completely contractive Banach algebra. We investigate whether the product of two elements of $M$ that are both weakly almost periodic functionals on $M_\ast$ is again weakly almost periodic. For that purpose, we establish the following factorization result: If $M$ and $N$ are injective von Neumann algebras, and if $x, y \in M \bar{\otimes} N$ correspond to weakly compact operators from $M_\ast$ to $N$ factoring through reflexive operator spaces $X$ and $Y$, respectively, then the operator corresponding to $xy$ factors through th…

Cohen strongly p-summing holomorphic mappings on Banach spaces

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 …

On composition ideals and dual ideals of bounded holomorphic mappings

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…

关于加权全纯函数空间中的p-可和性

On p-summability in weighted Banach spaces of holomorphic functions

本文研究了加权全纯映射的p-可和性类，证明其为注入Banach理想，并探讨了Pietsch定理、因子定理和Maurey外推定理的变体，以及p-可和全纯映射空间与Chevet-Saphar张量范数变体下的对偶空间的关系。

与p-紧型集相关的加权全纯映射

Weighted holomorphic mappings associated with p-compact type sets

本文引入并研究了与p-紧型集相关的加权全纯映射类，证明其可通过线性算子线性化刻画，构成由p-紧算子生成的Banach理想，并给出通过商空间分解及转置算子拟p-核性的等价刻画。

通过 Hilbert 空间分解的 Bloch 映射

Factorization of Bloch mappings through a Hilbert space

本文引入了复单位圆盘上通过 Hilbert 空间分解的向量值全纯映射概念，并系统阐述了此类 Bloch 映射空间在线性化、对偶性及 Banach 理想性质等方面的主要特征。

加权全纯映射理想的商

On quotients of ideals of weighted holomorphic mappings

本文研究加权全纯映射理想的左商过程，证明在若干算子理想下不产生新理想，但在其他情形（如格罗滕迪克和罗森塔尔加权全纯映射）可生成新的加权全纯理想。

Factorization and weak amenability of A(X)

We investigate weak amenability of the Banach algebra A(X) of approximable operators on a Banach space X and its relation to factorization properties of operators in A(X). We show that if A(X) is weakly amenable, then either A(X) is self-induced (a nice factorization property), or X is very special, combining some of the exotic properties of the spaces of Gowers and Maurey and of Pisier. In the class of self-induced Banach algebras we show that weak amenability is preserved under an equivalence of Morita type. Using this we extend some results of A. Blanco about weak amenability of A(X).

内函数逼近的膨胀理论方法

A dilation theoretic approach to approximation by inner functions

本文利用希尔伯特空间算子理论（酉膨胀、实现公式及多种分解）证明了单位圆盘和双圆盘上矩阵值全纯函数及J-压缩亚纯函数的逼近定理，推广了Carathéodory和Fisher的结果。