Scalable g-frame in Hilbert spaces

Document Type : Original Article


Faculty of Mathematical Sciences and Computer, Kharazmi University, 599 Taleghani Ave.


Tight frames and g-frames are extremely useful in applications. A scalable frame was recently
introduced as a frame with the property of generating a tight frame by rescaling its frame vectors. In this
paper, we generalize this concept to g-frames, introduce scalable g-frames, obtain some characterizations
for them, and demonstrate that scalability is stable under unitary operators and isomorophisms between
two Hilbert spaces. In addition, we consider Paley-Wiener perturbations of g-frames and achieve some
results regarding the preservation of their g-frame property.


Main Subjects

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