%0 Journal Article
%T On Sum and Stability of Continuous $G$-Frames
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Yousefzadeheyni, Azam
%A Abdollahpour, Mohammad Reza
%D 2020
%\ 01/01/2020
%V 17
%N 1
%P 157-169
%! On Sum and Stability of Continuous $G$-Frames
%K Continuous $g$-frame
%K Parseval continuous $g$-frame
%K Continuous $g$-Bessel family
%K stability
%R 10.22130/scma.2018.90101.472
%X 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.
%U http://scma.maragheh.ac.ir/article_37340_62593c31158dad0ce79ce0e6381dd264.pdf