On the duality of function valued frames in $L^2(0,\infty)$

Document Type : Research Paper

Authors

Department of Mathematical Sciences, Yazd University, Yazd, Iran

Abstract

By the notion of $F_a$-factorable operators, we establish a new version of the Riesz Representation Theorem adapted to this class of operators. Also, for $F_a$-factorable operators $T$ and $T^{\prime}$, we derive some equivalent conditions such that the equation $T^{\prime}=TX$ has a unique solution in the class of $F_a$-factorable operators. Moreover, by using the concept of $F_a$-frame in $L^2(0,\infty)$, which is similar yet distinct from the traditional frame concept, we establish optimal $F_a$-frame bounds, and provide a complete characterization of all corresponding $F_a$-dual frames.

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References

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History

  • Receive Date: 10 June 2025
  • Revise Date: 25 November 2025
  • Accept Date: 31 December 2025

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