Abstract:In this paper, we present some inequalities for sector matrices with negative
power. Among other results, we prove that if A,B ? Mn(C) with W(A),W(B) ?
S?, then for any positive unital linear map ?, it holds R((1-v)?(A) +
v?(B))r ? cos2r(?)R?((1-v)Ar + vBr), where v ? [0,1] and r ? [-1,0].
This improves Tan and Xie?s Theorem 2.4 in [22] if setting ?(X) = X for
every X ? Mn(C) and replacing A by A-1, B by B-1, respectively, and r=-1, which is also a special result of Bedrani, Kittaneh and Sababhe… Show more
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