چکیده
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The notation of generalized Bessel multipliers is obtained by a
bounded operator on 2 which is inserted between the analysis and synthesis
operators. We show that various properties of generalized multipliers
are closely related to their parameters, in particular, it will be shown that
the membership of generalized Bessel multiplier in the certain operator
classes requires that its symbol belongs in the same classes, in a special
sense. Also, we give some examples to illustrate our results. As we shall
see, generalized multipliers associated with Riesz bases are well-behaved,
more precisely in this case multipliers can be easily composed and inverted.
Special attention is devoted to the study of invertible generalized
multipliers. Sufficient and/or necessary conditions for invertibility are determined.
Finally, the behavior of these operators under perturbations is
discussed.
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