TY - JOUR
T1 - Toeplitz $O$-Frames for Operators in Banach Spaces
AU - Shekhar , Chander
AU - Kaushik , S. K.
JO - Analysis in Theory and Applications
VL - 4
SP - 363
EP - 373
PY - 2025
DA - 2025/02
SN - 40
DO - http://doi.org/10.4208/ata.OA-2017-0028
UR - https://global-sci.org/intro/article_detail/ata/23859.html
KW - Frames, operators, $O$-frames.
AB - <p style="text-align: justify;">We define Toeplitz $O$-frame for operators as a generalization of the notion
of $O$-frame introduced by Reinov [11]. A necessary condition for the existence of
a Toeplitz $O$-frame is given. It has been proved that an $O$-frame for operators can
generate a Toeplitz $O$-frame from a given Toeplitz matrix but the converse need not be
true. Also, a sufficient condition on infinite matrices for the existence of an $O$-frame is
given. Finally, the notion of a strong $O$-frame is defined and a necessary and sufficient
condition for its existence has been obtained.</p>