New norm equalities and inequalities for operator matrices

Abstract

Abstract We prove new inequalities for general 2 × 2 $2\times2$ 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 $5\times5$ tridiagonal operator matrix.

Keywords

• numerical radius
• usual operator norm
• operator matrix
• tridiagonal
• Jensen’s inequality
• mixed Schwarz inequality