Bohr’s inequalities for Hilbert space operators ✩

The classical Bohr’s inequality states that |z +w|2 p|z|2 + q|w|2 for all z,w ∈ C and all p, q > 1 with 1 p + 1 q = 1. In this paper, Bohr’s inequality is generalized to the context of Hilbert space operators for all positive conjugate exponents p, q ∈ R. In particular, the parallelogram law is recovered and some other interesting operator inequalities and established. © 2005 Elsevier Inc. All rights reserved.