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Coefficient multipliers on spaces of vector-valued entire Dirichlet series. (English) Zbl 06770147
Summary: The spaces of entire functions represented by Dirichlet series have been studied by Hussein and Kamthan and others. In the present paper we consider the space $$X$$ of all entire functions defined by vector-valued Dirichlet series and study the properties of a sequence space which is defined using the type of an entire function represented by vector-valued Dirichlet series. The main result concerns with obtaining the nature of the dual space of this sequence space and coefficient multipliers for some classes of vector-valued Dirichlet series.
##### MSC:
 30B50 Dirichlet series, exponential series and other series in one complex variable 30D15 Special classes of entire functions of one complex variable and growth estimates 46E40 Spaces of vector- and operator-valued functions
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