@Article{JNMA-6-1171,
author = {Chi , Xiujiao and Li , Pengtong},
title = {On Dual $K$-$g$-Bessel Sequences and $K$-$g$-Orthonormal Bases},
journal = {Journal of Nonlinear Modeling and Analysis},
year = {2024},
volume = {6},
number = {4},
pages = {1171--1185},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2562-2862},
doi = {https://doi.org/10.12150/jnma.2024.1171},
url = {http://global-sci.org/intro/article_detail/jnma/23678.html}
}