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

Liran Rotem

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

6 Scopus citations

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 (US)
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 - Jan 30 2016
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2016 American Institute of Mathematical Sciences.

Keywords

Banach limit
Convex bodies
Geometric mean

Publisher link

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 = "English (US)",

volume = "23",

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KW - Banach limit

KW - Convex bodies

KW - Geometric mean

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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

Bibliographical note

Keywords

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