Operator Bohr-Type inequalities

Abstract

The classical Bohr inequality for scalars was extended to the non-commutative case of Hilbert space operators in the literature. The sole goal of this article is to discuss the operator Bohr inequality and present some of its new variants. This includes fresh reverses and re nements of this inequality with applications towards an operators real and imaginary parts, not to forget the new discussion of di erent domains of the parameters. One further application towards the operator Dunkl-Williams inequality will be presented too. While the new results are interesting, we emphasize that the approach used to explore these inequalities di ers from the existing literature methods for this context.