MATRIX POWER MEANS AND PÓLYA--SZEGÖ TYPE INEQUALITIES

Abstract

t has been shown that if μ is a compactly supported probability measure on Mn+, then for every unit vector η∈ℂn, there exists a compactly supported probability measure (denoted by on ℝ+ so that the inequality ≤ Pt() (t∈(0,1]) holds. In particular, we consider a reverse of the above inequality and present some Pólya--Szegö type inequalities for power means of probability measures on positive matrices.

Keywords

• power means
• pólya--szegö inequality
• probability measure
• positive matrix