TY - JOUR
T1 - On Dual $K$-$g$-Bessel Sequences and $K$-$g$-Orthonormal Bases
AU - Chi , Xiujiao
AU - Li , Pengtong
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 1171
EP - 1185
PY - 2024
DA - 2024/12
SN - 6
DO - http://doi.org/10.12150/jnma.2024.1171
UR - https://global-sci.org/intro/article_detail/jnma/23678.html
KW - $K$-$g$-frames, dual $K$-$g$-Bessel sequences, $K$-$g$-orthonormal bases, $K$-$g$-Riesz bases.
AB - <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>