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The algebra of Bessel sequences and means of frames in Hilbert spaces. (English) Zbl 1474.42117

Summary: In this paper, a one-to-one correspondence between Bessel sequences and bounded linear operators is provided. This leads to an algebra structure on the set of all Bessel sequences in a separable Hilbert space. Some kinds of frames as special classes of operators are considered. Also, normal Bessel sequences and positive frames are presented. Finally, power means of positive frames are introduced. These allow researches to construct a large number of new frames from existing frames.

MSC:

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