Scalable g-frames and piecewise scalable frames in Hilbert spaces

Document Type : Original Article

Authors

1 Faculty of Mathematical Sciences and Computer, Kharazmi University, 599 Taleghani Ave., Tehran 15618, Iran

2 Faculty of Mathematical Sciences and Computer, Kharazmi University, 599 Taleghani Ave., Tehran 15618, Iran,

Abstract

In this paper, we generalize the concept of scalability to g-frames, introduce scalable g-frames, obtain some characterizations for them, and demonstrate that scalability is stable under unitary operators and isomorphisms between two Hilbert spaces. In addition, we consider and study the piecewise scalability of frames in Hilbert spaces.  In particular, we present some necessary and sufficient conditions for the piecewise scalability of frames in H, and we will extend this concept to the tensor product of Hilbert spaces.

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References

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Measure Algebras and Applications
Volume 2, Issue 1 - Serial Number 2
August 2024
Pages 104-118

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History

  • Receive Date: 03 April 2024
  • Revise Date: 16 June 2024
  • Accept Date: 22 June 2024

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