  In the present paper the unconditional convergence and the invertibility of
multipliers is investigated. Multipliers are operators created by (frame-like)
analysis, multiplication by a fixed symbol, and resynthesis. Sufficient and/or
necessary conditions for unconditional convergence and invertibility are
determined depending on the properties of the analysis and synthesis sequences,
as well as the symbol. Examples which show that the given assertions cover
different classes of multipliers are given. If a multiplier is invertible, a
formula for the inverse operator is determined. The case when one of the
sequences is a Riesz basis is completely characterized.
