Year: 2024
Author: Xiujiao Chi, Pengtong Li
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 4 : pp. 1171–1185
Abstract
In Hilbert spaces, $K$-$g$-frames are an advanced version of $g$-frames that enable the reconstruction of objects from the range of a bounded linear operator $K.$ This research investigates $K$-$g$-frames in Hilbert space. Firstly, using the $g$-preframe operators, we characterize the dual $K$-$g$-Bessel sequence of a $K$-$g$ frame. We provide additional requirements that must be met for the sum of a given $K$-$g$-frame and its dual $K$-$g$-Bessel sequence to be a $K$-$g$-frame. At the end of this paper, we present the concept of $K$-$g$-orthonormal bases and explain their link to $g$-orthonormal bases in Hilbert space. We also provide an alternative definition of $K$-$g$-Riesz bases using $K$-$g$-orthonormal bases. This gives a better understanding of the concept.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2024.1171
Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 4 : pp. 1171–1185
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: $K$-$g$-frames dual $K$-$g$-Bessel sequences $K$-$g$-orthonormal bases $K$-$g$-Riesz bases.