Banach limit in convexity and geometric means for convex bodies

Liran Rotem

doi:10.3934/era.2016.23.005

Banach limit in convexity and geometric means for convex bodies

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	41-51
Number of pages	11
Journal	Electronic Research Announcements in Mathematical Sciences
Volume	23
DOIs	https://doi.org/10.3934/era.2016.23.005
State	Published - 30 Jan 2016
Externally published	Yes

Keywords

Banach limit
Convex bodies
Geometric mean

All Science Journal Classification (ASJC) codes

General Mathematics

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10.3934/era.2016.23.005

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title = "Banach limit in convexity and geometric means for convex bodies",

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.",

keywords = "Banach limit, Convex bodies, Geometric mean",

author = "Liran Rotem",

note = "Publisher Copyright: {\textcopyright} 2016 American Institute of Mathematical Sciences.",

year = "2016",

month = jan,

day = "30",

doi = "10.3934/era.2016.23.005",

language = "الإنجليزيّة",

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KW - Convex bodies

KW - Geometric mean

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DO - 10.3934/era.2016.23.005

M3 - مقالة

SN - 1935-9179

VL - 23

SP - 41

EP - 51

JO - Electronic Research Announcements in Mathematical Sciences

JF - Electronic Research Announcements in Mathematical Sciences

ER -

Banach limit in convexity and geometric means for convex bodies

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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