On a loomis-whitney type inequality for permutationally invariant unconditional convex bodies

Piotr Nayar; Tomasz Tkocz

doi:10.1007/978-3-642-29849-3_19

On a loomis-whitney type inequality for permutationally invariant unconditional convex bodies

Piotr Nayar, Tomasz Tkocz

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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Abstract

For a permutationally invariant unconditional convex body K in K ⁿwe define a finite sequence (K_j)ⁿ _j=1of projections of the body K to the space spanned by first j vectors of the standard basis of Rⁿ We prove that the sequence of volumes (K_j)ⁿ_j=1 is log-concave.

Original language	English (US)
Title of host publication	Geometric Aspects of Functional Analysis
Subtitle of host publication	Israel Seminar 2006-2010
Publisher	Springer Verlag
Pages	327-333
Number of pages	7
ISBN (Print)	9783642298486
DOIs	https://doi.org/10.1007/978-3-642-29849-3_19
State	Published - 2012
Externally published	Yes

Publication series

Name	Lecture Notes in Mathematics
Volume	2050
ISSN (Print)	0075-8434

Bibliographical note

Funding Information:
The authors would like to thank Prof. K. Oleszkiewicz for a valuable comment regarding the equality conditions in Theorem as well as Prof. R. Latała for a stimulating discussion. Research of the First named author partially supported by NCN Grant no. 2011/01/N/ST1/01839. Research of the second named author partially supported by NCN Grant no. 2011/01/N/ST1/05960.

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AU - Tkocz, Tomasz

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AB - For a permutationally invariant unconditional convex body K in K nwe define a finite sequence (Kj)n j=1of projections of the body K to the space spanned by first j vectors of the standard basis of Rn We prove that the sequence of volumes (Kj)nj=1 is log-concave.

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ER -

On a loomis-whitney type inequality for permutationally invariant unconditional convex bodies

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