论文标题
Banach空间中的凸度，plurisubharmonicity和强大的最大模量原理
Convexity, plurisubharmonicity and the strong maximum modulus principle in Banach spaces
论文作者
论文摘要
在本文中，我们首先尝试更精确地使凸性和多毛的性类比更加精确。然后，我们介绍了类似于严格凸度的严格多元性概念的概念，并展示了如何使用该概念来研究Banach空间中强大的最大模量原理。作为应用程序，我们定义了一个$ l^p $直接整体的概念，其中包括Bochner $ l^p $空间，$ \ ell^p $ Direct Sugs和Hilbert Direct Direct积分，并且在适当的假设下，当$ p $ p $ Direct Mytimal andive Allive the Modiple andive y Modiple andive y Moduls y Modiply y Moduls均可在适当的假设下进行。该陈述可以被视为对几个已知结果的改写，但是严格的Plurisubharmonicity的概念产生了新的证明，这具有短暂，启发性和统一的优势。
In this article, we first try to make the known analogy between convexity and plurisubharmonicity more precise. Then we introduce a notion of strict plurisubharmonicity analogous to strict convexity, and we show how this notion can be used to study the strong maximum modulus principle in Banach spaces. As an application, we define a notion of $L^p$ direct integral of a family of Banach spaces, which includes at once Bochner $L^p$ spaces, $\ell^p$ direct sums and Hilbert direct integrals, and we show that under suitable hypotheses, when $p < \infty$, an $L^p$ direct integral satisfies the strong maximum modulus principle if and only if almost all members of the family do. This statement can be considered as a rewording of several known results, but the notion of strict plurisubharmonicity yields a new proof of it, which has the advantage of being short, enlightening and unified.
