NUMERICAL RANGE AND POSITIVE BLOCK MATRICES

초록

We obtain several norm and eigenvalue inequalities for positive matrices partitioned into four blocks. The results involve the numerical range W(X) of the off-diagonal block X, especially the distance d from 0 to W(X). A special consequence is an estimate, diamW([(A)(X*) (X)(B)]) - diamW(A + B/2) >= 2d, between the diameters of the numerical ranges for the full matrix and its partial trace.

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