Banach limit in convexity and geometric means for convex bodies | Zendy

Liran Rotem | Zendy

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Banach limit in convexity and geometric means for convex bodies

Author(s) -

Liran Rotem

Publication year - 2016

Publication title -

electronic research announcements

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.865

H-Index - 23

ISSN - 1935-9179

DOI - 10.3934/era.2016.23.005

Subject(s) - mathematics , convexity , regular polygon , mixed volume , limit (mathematics) , construct (python library) , pure mathematics , convex analysis , uniformly convex space , class (philosophy) , banach space , mathematical analysis , convex optimization , geometry , banach manifold , computer science , lp space , artificial intelligence , economics , financial economics , programming language

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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