Versions of Inequalities Related to p-Schatten Norm

Abstract

In this paper, we investigate some operator inequalities for the p-Schatten norm and obtain some other versions of these inequalities when parameters taking values in different regions. Let A1,…,An, B1,…,Bn∈BpH such that ∑i,j=1nAi∗Bj=0. Then, for p≥2, p≥λ>0, and 0<μ≤2, n21/p−1/λ∑i,j=1nAi±Bjpλ1/λ≤n1/2∑i=1nAi2+∑i=1nBi2p/21/2≤21/2−μ/4n1−μ/4∑i=1nAip4/μ+∑i=1nBip4/μμ/4. For 0<p≤2, p≤λ, and μ≥2, the inequalities are reversed. Moreover, we get some applications of our results.