Monotone substochastic operators and a new Calderon couple

2015/02/17 by Lesnik, Karol
#46B42 #46B70 #46E30 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1502.04882

Abstract

An important result on submajorization, which goes back to Hardy, Littlewood and Pólya, states that b\preceq a if and only if there is a doubly stochastic matrix A such that b=Aa. We prove that under monotonicity assumptions on vectors a and b respective matrix A may be chosen monotone. This result is then applied to show that (\widetildeL^p,L^∞) is a Calderón couple for 1≤ p

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