Subadditive inequalities for operators

2019/04/26 by Moradi, Hamid Reza, Heydarbeygi, Zahra, Sababheh, Mohammad
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1904.11880

Abstract

In this article, we present a new subadditivity behavior of convex and concave functions, when applied to Hilbert space operators. For example, under suitable assumptions on the spectrum of the positive operators A and B, we prove that 2^1-r( A+B )^r≤ A^r+B^r for rgt;1 and rlt;0, and A^r+B^r≤ 2^1-r( A+B )^r for r∈ [ 0,1 ]. These results provide considerable generalization of earlier results by Aujla and Silva. Further, we present several extensions of the subadditivity idea initiated by Ando and Zhan, then extended by Bourin and Uchiyama.

Related

• A matrix subadditivity inequality for f(A+B) and f(A)+f(B)
• New inequalities for operator concave functions involving positive linear maps
• Concave functions of positive operators, sums and congruences
• Matrix subadditivity inequalities and block-matrices
• A matrix subadditivity inequality for symmetric norms