TY - JOUR
ID - 37340
TI - On Sum and Stability of Continuous $G$-Frames
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Yousefzadeheyni, Azam
AU - Abdollahpour, Mohammad Reza
AD - Department of Mathematics, Faculty of Science, University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran.
Y1 - 2020
PY - 2020
VL - 17
IS - 1
SP - 157
EP - 169
KW - Continuous $g$-frame
KW - Parseval continuous $g$-frame
KW - Continuous $g$-Bessel family
KW - stability
DO - 10.22130/scma.2018.90101.472
N2 - In this paper, we give some conditions under which the finite sum of continuous $g$-frames is again a continuous $g$-frame. We give necessary and sufficient conditions for the continuous $g$-frames $Lambda=left{Lambda_w in Bleft(H,K_wright): win Omegaright}$ and $Gamma=left{Gamma_w in Bleft(H,K_wright): win Omegaright}$ and operators $U$ and $V$ on $H$ such that $Lambda U+Gamma V={Lambda_w U+Gamma_w V in Bleft(H,K_wright): win Omega}$ is again a continuous $g$-frame. Moreover, we obtain some sufficient conditions under which the finite sum of continuous $g$-frames are stable under small perturbations.
UR - http://scma.maragheh.ac.ir/article_37340.html
L1 - http://scma.maragheh.ac.ir/article_37340_62593c31158dad0ce79ce0e6381dd264.pdf
ER -