Algebraic Frames and Duality

Authors

  • Shahrzad Azadi
  • Mehdi Radjabalipour Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

DOI:

https://doi.org/10.30495/jme.v0i0.1516

Keywords:

Unbounded operators, algebraic frames, algebraic dual frame, dual frame, generalized frames.

Abstract

The theory of algebraic frames for a Hilbert space $H$ is a generalization of the theory of frames and generalized frames. The paper applies the theory of unbounded operators to define the dual of algebraic frames with densely defined unbounded analysis operators. It is shown that every algebraic frame has an algebraic dual frame, and if an algebraic frame has a nonzero redundancy, then it is not Riesz-type. An example of an algebraic frame with finite redundancy is constructed which is not a Riesz-type algebraic frame. Finally, for a lower bounded analytic frame, the discreteness of its indexing measure space and the uniqueness of its algebraic dual are studied and shown to be interrelated.

Author Biography

Mehdi Radjabalipour, Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

Full professor of mathematics

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Published

2020-07-22

Issue

Vol. 15

Section

Vol. 15, No. 3, (2021)

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