Abstract
In this paper, we investigate the known operator inequalities for the p-Schatten norm and obtain some refinements of these inequalities when parameters taking values in different regions. Let A1,...,An, B1,..., Bn ? Bp(H) such that ?ni,j=1Ai*Bj=0. Then p ? 2, p ? ? and ? ? 2, 21/p-?/4n3/p-?/4-1/2(?ni=1 ||Ai||4/?p + ?ni=1 ||Bi||4/?p )?/4 ? n2/p-1/2||?ni=1 |Ai|2 + ?ni=1 |Bi|2||1/2 p/2 ? n2/p-2/?(?ni,j=1 ||Ai ? Bj||?p)1/?. For 0 < p ? 2, p ? ? > 0 and 0 < ? ? 2, the inequalities are reversed. Moreover, we get some applications of our results.
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