Characterization of Banach algebras satisfying the von Neumann inequality

Characterize Banach algebras satisfying the von Neumann inequality.

Background

In the introduction, the authors note that Bohr’s inequality has connections to problems in Banach algebra theory. In particular, Dixon used Bohr’s inequality in relation to the long-standing problem of identifying which Banach algebras satisfy the von Neumann inequality.

Despite numerous advances in Bohr-type inequalities and their applications, a complete characterization of Banach algebras satisfying the von Neumann inequality remains unresolved.

References

In 1995, Dixon [16] used the Bohr inequality in connection with the long-standing open problem of character- izing Banach algebras satisfying the von Neumann inequality.

— The Bohr-type inequalities for holomorphic functions with lacunary series in complex Banach space (2404.18623 - Kumar et al., 29 Apr 2024) in Section 1.1: The classical Bohr inequality for the class B