Scalable g-frame in Hilbert spaces

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Khosravi Amir; Farmani Mohammad Reza

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Journal Paper

Paper Information

Journal: Mathematics and Computational Sciences Year:2023 | Volume:4 | Issue:3 Page(s): 19-27

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Information Journal Paper

Title

Scalable g-frame in Hilbert spaces

Author(s)

Khosravi Amir | Farmani Mohammad Reza | Issue Writer Certificate

Keywords

Frame

Frame operator

G-Frame

scalable

Hilbert space

Abstract

Tight Frames and g-Frames are extremely useful in applications. A scalable Frame was recentlyintroduced as a Frame with the property of generating a tight Frame by rescaling its Frame vectors. In thispaper, we generalize this concept to g-Frames, introduce scalable g-Frames, obtain some characterizationsfor them, and demonstrate that scalability is stable under unitary operators and isomorophisms betweentwo Hilbert spaces. In addition, we consider Paley-Wiener perturbations of g-Frames and achieve someresults regarding the preservation of their g-Frame property.

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