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SOME OPERATOR INEQUALITIES ON SCHUR PRODUCT AND MATRIX WEIGHTED GEOMETRIC MEAN

HUARONG WANG

Published Jan 1, 2026• 0 citations
Publisher

Abstract

We complement some properties on operator inequality related to Schur product. Then we discuss the inequalities around the matrix weighted geometric mean, and giveΦ(B]tA) ≤ Φ(B)]tΦ(A);for any positive and unital linear map Φ. Further, if mI ≤ A; B ≤ MI, thenΦ(A]tB) ≥ 4mM(M + m)2 Φ(A)]tΦ(B):
DOI
10.5281/zenodo.19606284

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