Generalized multipliers of controlled sequences

In this paper, we introduce a general version of multipliers for controlled sequences. In fact, by combining analysis, an operator on the Hilbert space ℓ۲(I) and synthesis, we reach so-called generalized controlled Bessel multipliers. Some basic properties of this class of operators are investigated. Specially, we are interested to determine cases when generalized multipliers are invertible. Subsequently, our attention is on how to express the inverse of an invertible generalized frame multiplier as a multiplier.

کلیدواژه ها:

Controlled frames ، Controlled Riesz bases ، Bessel multipliers