Volume 11, Issue 1 (4-2016)                   IJMSI 2016, 11(1): 57-67 | Back to browse issues page

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Abdollahi A, Rahimi E. Stability of $g$-Frame Expansions. IJMSI. 2016; 11 (1) :57-67
URL: http://ijmsi.ir/article-1-587-en.html

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 $beta$.

Type of Study: Research paper | Subject: Special

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