CONTROLLED K-FRAMES IN HILBERT C*-MODULES
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Controlled frames have been the subject of interest because of their ability to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper, we introduce the notion of controlled $K$-frame or controlled operator frame in Hilbert $C^{*}$-modules. We establish the equivalent condition for controlled $K$-frame. We investigate some operator theoretic characterizations of controlled $K$-frames and controlled Bessel sequences. Moreover, we establish the relationship between the $K$-frames and controlled $K$-frames. We also investigate the invariance of a controlled $K$-frame under a suitable map $T$. At the end, we prove a perturbation result for controlled $K$-frame.
Abstract
Controlled frames have been the subject of interest because of their ability to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper, we introduce the notion of controlled $K$-frame or controlled operator frame in Hilbert $C^{*}$-modules. We establish the equivalent condition for controlled $K$-frame. We investigate some operator theoretic characterizations of controlled $K$-frames and controlled Bessel sequences. Moreover, we establish the relationship between the $K$-frames and controlled $K$-frames. We also investigate the invariance of a controlled $K$-frame under a suitable map $T$. At the end, we prove a perturbation result for controlled $K$-frame.
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