On the Bohr inequality of operators

This paper is focused on the operator inequalities of the Bohr type. We will give a new and transparent proof for the operator Bohr inequality through an absolute value operator identity, show some related operator inequalities by means of 2 × 2 (block) operator matrices, and finally we will present a generalization of the operator Bohr inequality for multiple operators. © 2006 Elsevier Inc. All rights reserved.