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Properties of frame mappings devised by controlled p-frames and p-frames. (English) Zbl 1459.42046

Summary: p-frames in Banach spaces are straightforward generalization of frames in Hilbert spaces. In this paper, motivated the concept of p-Bessel sequences, the concept of p-controlled Bessel sequences is introduced and showed that under some warily conditions, \(1<\text{p}\leq 2\), they can use instead of each other. Also a close relationship between inherent properties of p-frame mappings and p-pseudo frame mappings with controlled p-frames and p-frames is found. In other words the cases that these natural mappings can be accretive, Lipschitz continuous, coercive and monotone are investigated.

MSC:

42C15 General harmonic expansions, frames
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
47H05 Monotone operators and generalizations
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References:

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