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On bi-Banach frames in Banach spaces. (English) Zbl 1290.42061

The author provides a necessary and sufficient condition for a Banach space \(E\) to have a bi-Banach frame in terms of i) a retro Banach frame, and ii) weak\(^*\) topology of the conjugate space \(E^*\). Examples and counterexamples are provided. The author also proves that if the two Banach spaces \(E^*\) and \(F^*\) both have pseudo exact retro Banach frames, so does the product space \((E\times F)^*\).

MSC:

42C15 General harmonic expansions, frames
42C30 Completeness of sets of functions in nontrigonometric harmonic analysis
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