Banach limit in convexity and geometric means for convex bodies

Q3 Mathematics

Electronic Research Announcements in Mathematical Sciences Pub Date : 2016-11-01 DOI:10.3934/ERA.2016.23.005

Liran Rotem

引用次数: 6

Abstract

In this note we construct Banach limits on the class of sequences of convex bodies. Surprisingly, the construction uses the recently introduced geometric mean of convex bodies. In the opposite direction, we explain how Banach limits can be used to construct a new variant of the geometric mean that has some desirable properties.

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凸性的Banach极限与凸体的几何均值

本文构造了一类凸体序列的Banach极限。令人惊讶的是，该建筑使用了最近引入的凸体几何平均值。在相反的方向上，我们解释了如何使用巴拿赫极限来构造具有一些理想性质的几何平均值的新变体。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Electronic Research Announcements in Mathematical Sciences 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Electronic Research Archive (ERA), formerly known as Electronic Research Announcements in Mathematical Sciences, rapidly publishes original and expository full-length articles of significant advances in all branches of mathematics. All articles should be designed to communicate their contents to a broad mathematical audience and must meet high standards for mathematical content and clarity. After review and acceptance, articles enter production for immediate publication. ERA is the continuation of Electronic Research Announcements of the AMS published by the American Mathematical Society, 1995—2007