  This paper introduces the concept of Bessel multipliers. These operators are
defined by a fixed multiplication pattern, which is inserted between the
Analysis and synthesis operators. The proposed concept unifies the approach
used for Gabor multipliers for arbitrary analysis/synthesis systems, which form
Bessel sequences, like wavelet or irregular Gabor frames. The basic properties
of this class of operators are investigated. In particular the implications of
summability properties of the symbol for the membership of the corresponding
operators in certain operator classes are specified. As a special case the
multipliers for Riesz bases are examined and it is shown that multipliers in
this case can be easily composed and inverted. Finally the continuous
dependence of a Bessel multiplier on the parameters (i.e. the involved
sequences and the symbol in use) is verified, using a special measure of
similarity of sequences.
