A Simple Proof of Bohr's Inequality

TL;DR

This paper presents a straightforward and concise proof of Bohr's inequality, a fundamental result in complex analysis with implications for operator algebra theory.

Contribution

The paper offers a simple, accessible proof of Bohr's inequality, enhancing understanding and potential applications in functional analysis.

Findings

Proof of Bohr's inequality is shorter and easier to understand.

Reinforces the importance of Bohr's inequality in operator algebra theory.

Clarifies the relationship between bounded holomorphic functions and von Neumann inequalities.

Abstract

The classical inequality of Bohr concerning Taylor coeficients of bounded holomorphic functions on the unit disk, has proved to be of significance in answering in the negative the conjecture that if the non-unital von Neumann inequality held for a Banach algebra then it was necessarily an operator algebra. Here we provide a rather short and easy proof of the inequality.