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.
|Original language||English (US)|
|Title of host publication||Geometric Aspects of Functional Analysis|
|Subtitle of host publication||Israel Seminar 2006-2010|
|Number of pages||7|
|State||Published - 2012|
|Name||Lecture Notes in Mathematics|
Bibliographical noteFunding Information:
The authors would like to thank Prof. K. Oleszkiewicz for a valuable comment regarding the equality conditions in Theorem 1 as well as Prof. R. Lata?a 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.