Abstract:In this paper, we investigate the sums of Hilbert module frames. Several results on the sums of modular frames (Bessel sequences) being still frames are given.
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In this paper, we introduce the concept of K-dual. We investigate the K-duals that are optimal for erasures for Parseval K-frames in finite Hilbert spaces. We will give the necessary and sufficient conditions under which the canonical K-dual is the unique optimal K-duals for erasures. We also discuss some special conditions under which the canonical K-dual is not the optimal K-dual or optimal K-dual but not the unique one.
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