Spaces of vector-valued Dirichlet series in a half plane

Abstract

Dirichlet series with real frequencies which represent entire functions on the complex plane ℂ have been investigated by many authors. Several properties such as topological structures, linear continuous functionals, and bases have been considered. Le Hai Khoi derived some results with Dirichlet series having negative real frequencies which represent holomorphic functions in a half plane. In the present paper, we have obtained some properties of holomorphic Dirichlet series having positive exponents, whose coefficients belong to a Banach algebra.