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A note on O-frames for operators. (English) Zbl 1372.42031

Summary: A sufficient condition for a boundedly complete O-frame and a necessary condition for an unconditional O-frame are given. Also, a necessary and sufficient condition for an absolute O-frame is obtained. Finally, it is proved that if two operators have an absolute O-frame, then their product also has an absolute O-frame.

MSC:

42C15 General harmonic expansions, frames
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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