عنوان مجله
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Azerbaijan Journal of Mathematics
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کلیدواژهها
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Frame, Bessel sequence, Riesz basis, Hilbert C∗-module,
Multiplier operator.
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چکیده
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Multipliers are operators which have important applications for signal processing and acoustics. In this paper, we investigate invertibility of multipliers and Riesz
multipliers in Hilbert C∗-modules. We show, unlike to Riesz multipliers in Hilbert spaces,
Riesz multipliers in Hilbert C∗-modules may not be invertible. In addition, by using the
modular Riesz bases and uniqueness of dual, we characterize those Riesz bases in Hilbert
C∗-modules that their Riesz multipliers are invertible. Also, we obtain some necessary
conditions for invertibility of multipliers in Hilbert C∗-modules. Furthermore we show,
by using of dual frames, the inverse of any invertible multiplier operator in Hilbert C∗-
module is a multiplier operator.
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