Multipliers for p-Bessel Sequences in Banach Spaces

Rahimi, Asghar; Balázs, Péter

doi:10.1007/s00020-010-1814-7

Cited by 30 publications

(24 citation statements)

References 29 publications

(28 reference statements)

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“…They have been investigated for Gabor frames [6–8], for fusion frames [9], for generalized frames [10], for

p

-frames in Banach spaces [11] and continuous frames [12]. The concept of multipliers is naturally related to weighted frames [13,3] as well as to matrix representation of operators [14].…”

Section: Introductionmentioning

confidence: 99%

Canonical forms of unconditionally convergent multipliers

Stoeva

Balázs

2013

Journal of Mathematical Analysis and Applications

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Multipliers are operators that combine (frame-like) analysis, a multiplication with a fixed sequence, called the symbol, and synthesis. They are very interesting mathematical objects that also have a lot of applications for example in acoustical signal processing. It is known that bounded symbols and Bessel sequences guarantee unconditional convergence. In this paper we investigate necessary and equivalent conditions for the unconditional convergence of multipliers. In particular, we show that, under mild conditions, unconditionally convergent multipliers can be transformed by shifting weights between symbol and sequence, into multipliers with symbol (1) and Bessel sequences (called multipliers in canonical form).

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“…They have been investigated for Gabor frames [6–8], for fusion frames [9], for generalized frames [10], for

p

-frames in Banach spaces [11] and continuous frames [12]. The concept of multipliers is naturally related to weighted frames [13,3] as well as to matrix representation of operators [14].…”

Section: Introductionmentioning

confidence: 99%

Canonical forms of unconditionally convergent multipliers

Stoeva

Balázs

2013

Journal of Mathematical Analysis and Applications

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“…Multipliers have been investigated for Bessel fusion sequences in Hilbert spaces [16] (called Bessel fusion multipliers) and for generalized Bessel sequences in Hilbert spaces [23] (called g-Bessel multipliers). Also multipliers were introduced for p-Bessel sequences in Banach spaces [24] and for continuous frames [6]. Recently the present author and A. Khosravi generalized Bessel multipliers, g-Bessel multipliers and Bessel fusion multipliers to Hilbert C * −modules and many important results obtained for Bessel multipliers in Hilbert and Banach spaces were generalized to Hilbert C * −modules (see [14]).…”

Section: Introductionmentioning

confidence: 97%

Invertibility of multipliers in Hilbert C*-modules

Morteza¹

2018

Filomat

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In this paper, we present some sufficient conditions under which Bessel multipliers in Hilbert C * −modules with semi-normalized symbols are invertible and we calculate the inverses. Especially we consider the invertibility of Bessel multipliers when the elements of their symbols are positive and when their Bessel sequences are equivalent, duals, modular Riesz bases or stable under small perturbations. We show that in these cases the inverse of a Bessel multiplier can be represented as a Bessel multiplier.

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“…[3,18,13], but they are also used in applications, in particular in the field of audio and acoustic. They have been investigated for fusion frames [1], for generalized frames [29], p-frames in Banach spaces [30] and for Banach frames [16,17]. In signal processing they are used for Gabor frames under the name of Gabor filters [23], in computational auditory scene analysis they are known by the name of time-frequency masks [24].…”

Section: Introductionmentioning

confidence: 99%

Controlled G-Frames and Their G-Multipliers in Hilbert spaces

Rahimi

Fereydooni

2013

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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Multipliers have been recently introduced by P. Balazs as operators for Bessel sequences and frames in Hilbert spaces. These are operators that combine (frame-like) analysis, a multiplication with a fixed sequence ( called the symbol) and synthesis. One of the last extensions of frames is weighted and controlled frames that introduced by P.Balazs, J-P. Antoine and A. Grybos to improve the numerical efficiency of iterative algorithms for inverting the frame operator. Also g-frames are the most popular generalization of frames that include almost all of the frame extensions. In this manuscript the concept of the controlled gframes will be defined and we will show that controlled g-frames are equivalent to g-frames and so the controlled operators C and C can be used as preconditions in applications. Also the multiplier operator for this family of operators will be introduced and some of its properties will be shown.

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Multipliers for p-Bessel Sequences in Banach Spaces

Cited by 30 publications

References 29 publications

Canonical forms of unconditionally convergent multipliers

Canonical forms of unconditionally convergent multipliers

Invertibility of multipliers in Hilbert C*-modules

Controlled G-Frames and Their G-Multipliers in Hilbert spaces

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