This is an announcement for the paper "Abscissas of weak convergence of vector valued Dirichlet series" by Jose Bonet.

Abstract: The abscissas of convergence, uniform convergence and absolute convergence of vector valued Dirichlet series with respect to the original topology and with respect to the weak topology $\sigma(X,X')$ of a locally convex space $X$, in particular of a Banach space $X$, are compared. The relation of their coincidence with geometric or topological properties of the underlying space $X$ is investigated. Cotype in the context of Banach spaces, and nuclearity and certain topological invariants for Fr'echet spaces play a relevant role.

Archive classification: math.FA

Mathematics Subject Classification: Primary: 46A04, secondary: 30B50, 32A05, 46A03, 46A11, 46B07

Submitted from: jbonet@mat.upv.es

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1502.00418

or

http://arXiv.org/abs/1502.00418