Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 11, Number 4 (2017), 880-898.
Duality properties for generalized frames
We introduce the concept of Riesz-dual sequences for g-frames. In this paper we show that, for any sequence of operators, we can construct a corresponding sequence of operators with a kind of duality relation between them. This construction is used to prove duality principles in g-frame theory, which can be regarded as general versions of several well-known duality principles for frames. We also derive a simple characterization of a g-Riesz basic sequence as a g-R-dual sequence of a g-frame in the tight case.
Banach J. Math. Anal., Volume 11, Number 4 (2017), 880-898.
Received: 22 July 2016
Accepted: 9 December 2016
First available in Project Euclid: 29 August 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 41A58: Series expansions (e.g. Taylor, Lidstone series, but not Fourier series) 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Secondary: 42C15: General harmonic expansions, frames 42C40: Wavelets and other special systems
Enayati, F.; Asgari, M. S. Duality properties for generalized frames. Banach J. Math. Anal. 11 (2017), no. 4, 880--898. doi:10.1215/17358787-2017-0027. https://projecteuclid.org/euclid.bjma/1503993619