Versions of Inequalities Related to p-Schatten Norm. (24th February 2020) - Gao, Fugen; Liu, Xiaoxiao; Tian, Mengyu
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 A 1, …, A n, B 1, …, B n ∈ B p H such that ∑ i, j = 1 n A i ∗ B j = 0 . Then, for p ≥ 2, p ≥ λ > 0, and 0 < μ ≤ 2, n 2 1 / p − 1 / λ ∑ i, j = 1 n A i ± B j p λ 1 / λ ≤ n 1 / 2 ∑ i = 1 n A i 2 + ∑ i = 1 n B i 2 p / 2 1 / 2 ≤ 2 1 / 2 − μ / 4 n 1 − μ / 4 ∑ i = 1 n A i p 4 / μ + ∑ i = 1 n B i p 4 / μ μ / 4 . For 0 < p ≤ 2, p ≤ λ, and μ ≥ 2, the inequalities are reversed. Moreover, we get some applications of our results.