Iranian Journal of Mathematical Sciences and Informatics
مجله علوم ریاضی و انفورماتیک
IJMSI
Basic Sciences
http://ijmsi.ir
1
admin
1735-4463
2008-9473
8
10.61186/ijmsi
14
8888
13
en
jalali
1395
1
1
gregorian
2016
4
1
11
1
online
1
fulltext
en
Stability of $g$-Frame Expansions
تخصصي
Special
پژوهشي
Research paper
<p>In this paper we investigate the stability of one-sided perturbation to g-frame expansions. We show that if $Lambda$ is a g-frame of a Hilbert space $mathcal{H}$, $Lambda_{i}^{a}=Lambda_{i}+Theta_{i}$ where $Theta_{i} in mathcal{L}(mathcal{H},mathcal{H}_{i})$, and $widetilde{f}=sum_{i in J}Lambda_{i}^{star}widetilde{Lambda}_{i}^{a}f$, $widehat{f}=sum_{i in J}(Lambda_{i}^{a})^{star}widetilde{Lambda_{i}}f$, then $|widehat{f}-f|leq alpha |f|$ and $|f-widetilde{f}|leq beta |f|$ for some $alpha$ and $beta$.</p>
g-Frames, g-Riesz bases, g-Orthonormal bases, Dual g-frames.
57
67
http://ijmsi.ir/browse.php?a_code=A-10-871-1&slc_lang=en&sid=1
A.
Abdollahi
abdollahi@shirazu.ac.ir
10031947532846002882
10031947532846002882
Yes
Shiraz University
E.
Rahimi
rahimie@shirazu.ac.ir
10031947532846002883
10031947532846002883
No
DepaShiraz Branch, Islamic Azad University