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Uniform excess of g-frames

  • Ahmad Ahmadi EMAIL logo und Abbas Askarizadeh
Veröffentlicht/Copyright: 25. Juli 2023
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Georgian Mathematical Journal
Aus der Zeitschrift Georgian Mathematical Journal Band 30 Heft 6

Abstract

Let { Λ i } i ∈ ℐ be a g-frame for 𝒰 with respect to { 𝒱 i } i ∈ ℐ , where 𝒰 and { 𝒱 i } i ∈ ℐ are Hilbert spaces. The excess of { Λ i } i ∈ ℐ is the largest cardinal number of the subsets 𝒥 of ℐ such that { Λ i } i ∈ ℐ ∖ 𝒥 is a g-frame for 𝒰 with respect to { 𝒱 i } i ∈ ℐ ∖ 𝒥 . In this paper, we consider the excess of a g-frame and introduce the concept of m-uniform excess for g-frames. Also, we present constructions of m-uniform excess g-frames. Finally, we investigate the relationship between m-uniform excess g-frames and woven g-frames.

Keywords: Uniform excess; full spark; woven frames
MSC 2020: 42C15; 46B28

Acknowledgements

The authors are grateful to the referees for their careful reading and useful comments.

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Received: 2022-12-08
Revised: 2023-01-19
Accepted: 2023-01-25
Published Online: 2023-07-25
Published in Print: 2023-12-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. On left and right Browder elements in Banach algebra relative to a bounded homomorphism
  3. Uniform excess of g-frames
  4. On normal partial isometries
  5. Gauss--Newton--Kurchatov method for the solution of non-linear least-square problems using ω-condition
  6. Maps preserving the bi-skew Jordan product on factor von Neumann algebras
  7. Boundary contact problems with regard to friction of couple-stress viscoelasticity for inhomogeneous anisotropic bodies (quasi-static cases)
  8. On uniform statistical convergence
  9. Approximate solution of the optimal control problem for non-linear differential inclusion on the semi-axes
  10. Energy-based localization of positive solutions for stationary Kirchhoff-type equations and systems
  11. e-reversibility of rings via quasinilpotents
  12. Weighted generalized Moore–Penrose inverse
  13. On two extensions of the annihilating-ideal graph of commutative rings
  14. Umbral treatment and lacunary generating function for Hermite polynomials
  15. A generalization of the canonical commutation relation and Heisenberg uncertainty principle for the orbital operators
https://doi.org/10.1515/gmj-2023-2049
Schlagwörter für diesen Artikel
Uniform excess; full spark; woven frames

Artikel in diesem Heft

  1. Frontmatter
  2. On left and right Browder elements in Banach algebra relative to a bounded homomorphism
  3. Uniform excess of g-frames
  4. On normal partial isometries
  5. Gauss--Newton--Kurchatov method for the solution of non-linear least-square problems using ω-condition
  6. Maps preserving the bi-skew Jordan product on factor von Neumann algebras
  7. Boundary contact problems with regard to friction of couple-stress viscoelasticity for inhomogeneous anisotropic bodies (quasi-static cases)
  8. On uniform statistical convergence
  9. Approximate solution of the optimal control problem for non-linear differential inclusion on the semi-axes
  10. Energy-based localization of positive solutions for stationary Kirchhoff-type equations and systems
  11. e-reversibility of rings via quasinilpotents
  12. Weighted generalized Moore–Penrose inverse
  13. On two extensions of the annihilating-ideal graph of commutative rings
  14. Umbral treatment and lacunary generating function for Hermite polynomials
  15. A generalization of the canonical commutation relation and Heisenberg uncertainty principle for the orbital operators
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