  We study star product algebras of analytic functions for which the power
series defining the products converge absolutely. Such algebras arise naturally
in deformation quantization theory and in noncommutative quantum field theory.
We consider different star products in a unifying way and present results on
the structure and basic properties of these algebras, which are useful for
applications. Special attention is given to the Hilbert space representation of
the algebras and to the exact description of their corresponding operator
algebras.
