Arithmetic Bohr radius of bounded linear operators

TL;DR

This paper explores the arithmetic Bohr radius for bounded linear operators on complex Banach spaces, establishing its relation to classical Bohr radius and analyzing its asymptotic behavior in various contexts.

Contribution

It introduces the concept of arithmetic Bohr radius for operators and provides asymptotic estimates, extending classical results to infinite-dimensional and sequence space settings.

Findings

Connected classical and arithmetic Bohr radii.

Derived asymptotic estimates for identity operators.

Determined asymptotic behavior of Bohr radii in sequence spaces.

Abstract

In this paper, we investigate the arithmetic Bohr radius of bounded linear operators between arbitrary complex Banach spaces. We establish the close connection between the classical Bohr radius and the arithmetic Bohr radius of bounded linear operators. Further, we study the asymptotic estimates of arithmetic Bohr radius for identity operator on infinite dimensional complex Banach spaces. Finally, we obtain the correct asymptotic behavior of Bohr radii of operators between sequence spaces.