On an entire function represented by multiple Dirichlet series

summary:Consider the space $L$ of entire functions represented by multiple Dirichlet series that becomes a non uniformly convex Banach space which is also proved to be dense, countable and separable. Continuing further, for the given space $L$ the characterization of bounded linear transformations in terms of matrix and characterization of linear functional has been obtained

On a class of vector-valued entire Dirichlet series in n variables

We consider a class F of entire Dirichlet series in n variables, whose coefficients belong to a commutative Banach algebra E. With a well defined norm, F is proved to be a Banach algebra with identity. Further results on quasi-invertibility, spectrum and continuous linear functionals are proved for elements belonging to F