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Asghar Rahimi

Asghar Rahimi

Academic rank: Professor
ORCID:
Education: PhD.
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Faculty: 1
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Research

Title
THE ALGEBRA OF BESSEL SEQUENCES AND MEANS OF FRAMES IN HILBERT SPACES
Type
JournalPaper
Keywords
Bessel sequence, positive frame, frame operator, means of frames
Year
2020
Journal Miskolc Mathematical Notes
DOI
Researchers Esmaiel Alizadeh ، Asghar Rahimi ، Mortaza Rahmani

Abstract

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.