Advanced refinements of Young and Heinz inequalities

2016/06/22 by Sababheh, Mohammad, Moslehian, Mohammad Sal
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1606.06848

Abstract

In this article, we prove several multi-term refinements of Young type inequalities for both real numbers and operators improving several known results. Among other results, we prove A#_νBamp;+amp;∑_j=1^Ns_j(ν)(A#_αj(ν)B+A#_{2^1-j+αj(ν)}B-2A#_2^-j+αj(ν)B)≤ A∇_νB, for the positive operators A and B, where 0≤ ν≤ 1, N∈ℕ and α_j(ν) is a certain function. Moreover, some new Heinz type inequalities involving the Hilbert-Schmidt norm are established.

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