We prove new norm equalities and inequalities for general n × n tridiagonal and antitridiagonal operator matrices, including pinching type inequalities for weakly unitarily invariant norms.

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We prove new inequalities for general 2 × 2 operator matrices. These inequalities, which are based on classical convexity inequalities, generalize earlier inequalities for sums of operators. Some other related results are also presented. Also, we prove a numerical radius equality for a 5 × 5 tridiagonal operator matrix.MSC: 47A12; 47A30; 47A63; 47B15; 47B36

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