论文标题
矢量测量和应用到可集成函数空间的等距分解
Isometric factorization of vector measures and applications to spaces of integrable functions
论文作者
论文摘要
令$ x $为Banach空间，$σ$为$σ$ -Algebra，而$ m：σ\ to x $是一个（可计算的）向量度量。这是戴维斯 - 外观 - 约翰逊 - 佩尔克兹基（Davis-Figiel-Johnson-Pelczýnski）分解过程的众所周知的后果，即存在反射性的banach空间$ y $，矢量测量$ \ tilde {m}：σ\ to y $ to y $和iendive opentive opertive operator $ j：y \ y \ y \ to x $ x $ y $ m $ m $ m = j $ m =我们借助戴维斯 - 外观 - 约翰逊 - 佩尔奇斯基分解过程的等距版本的帮助版本阐述了一些分解矢量测量及其集成运算符的理论。沿着这种方式，我们将冈田和Ricker的结果提高，如果$ l_1（m）$上的集成运算符是弱紧凑的，那么$ l_1（m）$是相等的，直至标准等同于标准，则在某些$ l_1（\ tilde m）上，$ y $ y $是反射的；在这里，我们证明可以将上述平等视为等距。
Let $X$ be a Banach space, $Σ$ be a $σ$-algebra, and $m:Σ\to X$ be a (countably additive) vector measure. It is a well known consequence of the Davis-Figiel-Johnson-Pelczýnski factorization procedure that there exist a reflexive Banach space $Y$, a vector measure $\tilde{m}:Σ\to Y$ and an injective operator $J:Y \to X$ such that $m$ factors as $m=J\circ \tilde{m}$. We elaborate some theory of factoring vector measures and their integration operators with the help of the isometric version of the Davis-Figiel-Johnson-Pelczýnski factorization procedure. Along this way, we sharpen a result of Okada and Ricker that if the integration operator on $L_1(m)$ is weakly compact, then $L_1(m)$ is equal, up to equivalence of norms, to some $L_1(\tilde m)$ where $Y$ is reflexive; here we prove that the above equality can be taken to be isometric.
