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

Mathematics

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

5 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

Keywords

Banach limit
Convex bodies
Geometric mean

Access

10.3934/era.2016.23.005

Fingerprint Dive into the research topics of 'Banach limit in convexity and geometric means for convex bodies'. Together they form a unique fingerprint.

Cite this

@article{ac5842818c7942398fa5f9a6d74d10e5,

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",

year = "2016",

month = jan,

day = "30",

doi = "10.3934/era.2016.23.005",

language = "English (US)",

volume = "23",

pages = "41--51",

journal = "Electronic Research Announcements in Mathematical Sciences",

issn = "1935-9179",

publisher = "American Mathematical Society",

}

TY - JOUR

T1 - Banach limit in convexity and geometric means for convex bodies

AU - Rotem, Liran

PY - 2016/1/30

Y1 - 2016/1/30

N2 - 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.

AB - 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.

KW - Banach limit

KW - Convex bodies

KW - Geometric mean

UR - http://www.scopus.com/inward/record.url?scp=85006818092&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85006818092&partnerID=8YFLogxK

U2 - 10.3934/era.2016.23.005

DO - 10.3934/era.2016.23.005

M3 - Article

AN - SCOPUS:85006818092

VL - 23

SP - 41

EP - 51

JO - Electronic Research Announcements in Mathematical Sciences

JF - Electronic Research Announcements in Mathematical Sciences

SN - 1935-9179

ER -