Open Access
January 2018 Generalized frames for operators associated with atomic systems
Dongwei Li, Jinsong Leng, Tingzhu Huang
Banach J. Math. Anal. 12(1): 206-221 (January 2018). DOI: 10.1215/17358787-2017-0050


In this paper, we investigate the g-frame and Bessel g-sequence related to a linear bounded operator K in Hilbert space, which we call a K-g-frame and a K-dual Bessel g-sequence, respectively. Since the frame operator for a K-g-frame may not be invertible, there is no classical canonical dual for a K-g-frame. So we characterize the concept of a canonical K-dual Bessel g-sequence of a K-g-frame that generalizes the classical dual of a g-frame. Moreover, we use a family of linear operators to characterize atomic systems. We also consider the construction of new atomic systems from given ones and bounded operators.


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Dongwei Li. Jinsong Leng. Tingzhu Huang. "Generalized frames for operators associated with atomic systems." Banach J. Math. Anal. 12 (1) 206 - 221, January 2018.


Received: 7 December 2016; Accepted: 31 March 2017; Published: January 2018
First available in Project Euclid: 5 December 2017

zbMATH: 1382.42019
MathSciNet: MR3745581
Digital Object Identifier: 10.1215/17358787-2017-0050

Primary: 42C15
Secondary: ‎42C40 , 47B32

Keywords: atomic system , canonical K-dual Bessel g-sequence , K-dual Bessel g-sequence , K-g-frames

Rights: Copyright © 2018 Tusi Mathematical Research Group

Vol.12 • No. 1 • January 2018
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