@article {
author = {Yousefzadeheyni, Azam and Abdollahpour, Mohammad Reza},
title = {On Sum and Stability of Continuous $G$-Frames},
journal = {Sahand Communications in Mathematical Analysis},
volume = {17},
number = {1},
pages = {157-169},
year = {2020},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2018.90101.472},
abstract = {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 $\Lambda=\left\{\Lambda_w \in B\left(H,K_w\right): w\in \Omega\right\}$ and $\Gamma=\left\{\Gamma_w \in B\left(H,K_w\right): w\in \Omega\right\}$ and operators $U$ and $V$ on $H$ such that $\Lambda U+\Gamma V=\{\Lambda_w U+\Gamma_w V \in B\left(H,K_w\right): w\in \Omega\}$ 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.},
keywords = {Continuous $g$-frame,Parseval continuous $g$-frame,Continuous $g$-Bessel family,stability},
url = {http://scma.maragheh.ac.ir/article_37340.html},
eprint = {http://scma.maragheh.ac.ir/article_37340_62593c31158dad0ce79ce0e6381dd264.pdf}
}