# Bohr phenomenon for operator valued functions

## TL;DR

This paper extends Bohr inequalities to operator-valued functions, providing new bounds and insights that generalize classical scalar results and explore the operator Bohr radius.

## Contribution

It introduces Bohr inequalities for operator-valued functions, broadening the scope of classical scalar Bohr inequalities to the operator setting.

## Key findings

- Established Bohr inequalities for operator-valued functions.
- Generalized the concept of the Bohr radius to operators.
- Connected classical and operator-valued Bohr phenomena.

## Abstract

In this article we establish Bohr inequalities for operator valued functions, which can be viewed as the analogues of a couple of interesting results from scalar valued settings. Some results of this paper are motivated by the classical flavor of Bohr inequality, while the others are based on a generalized concept of the Bohr radius problem.