Approximate duals and nearly Parseval frames

Authors: MORTEZA MIRZAEE AZANDARYANI

Abstract: In this paper we introduce approximate duality of g-frames in Hilbert $C^\ast$-modules and we show that approximate duals of g-frames in Hilbert $C^\ast$-modules share many useful properties with those in Hilbert spaces. Moreover, we obtain some new results for approximate duality of frames and g-frames in Hilbert spaces; in particular, we consider approximate duals of $\varepsilon$-nearly Parseval and $\varepsilon$-close frames.

Keywords: Hilbert $C^\ast$-module, g-frame, frame, approximate duality, $\varepsilon$-nearly Parseval frame

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