TY - JOUR
ID - 37409
TI - Generalized Continuous Frames for Operators
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - .Shekhar, Chander
AU - Bhati, Sunayana
AU - Rathore, G.S.
AD - Department of Mathematics Indraprastha college for Women, University of Delhi, Delhi 110054, India.
AD - Department of Mathematics and Statistics, University college of Science, M.L.S. University, Udaipur, Rajasthan, India.
Y1 - 2020
PY - 2020
VL - 17
IS - 2
SP - 185
EP - 201
KW - Frames
KW - $K$-frames
KW - Continuous frames
DO - 10.22130/scma.2018.97329.523
N2 - In this note, the notion of generalized continuous K- frame in a Hilbert space is defined. Examples have been given to exhibit the existence of generalized continuous $K$-frames. A necessary and sufficient condition for the existence of a generalized continuous $K$-frame in terms of its frame operator is obtained and a characterization of a generalized continuous $K$-frame for $ mathcal{H} $ with respect to $ mu $ is given. Also, a sufficient condition for a generalized continuous $K$-frame is given. Further, among other results, we prove that generalized continuous $K$-frames are invariant under a linear homeomorphism. Finally, keeping in mind the importance of perturbation theory in various branches of applied mathematics, we study perturbation of $K$-frames and obtain conditions for the stability of generalized continuous $K$-frames.
UR - https://scma.maragheh.ac.ir/article_37409.html
L1 - https://scma.maragheh.ac.ir/article_37409_6c5ddb5008c0e3934c7fff932837d13d.pdf
ER -