Redundancy of Fusion Frames in Hilbert Spaces

Upon improving and extending the concept of redundancy of frames, we introduce the notion of redundancy of fusion frames, which is concerned with the properties of lower and upper redundancies. These properties are achieved by considering the minimum and maximum values of the redundancy function whi...

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Bibliographic Details
Published inComplex analysis and operator theory Vol. 10; no. 3; pp. 545 - 565
Main Authors Rahimi, A., Zandi, G., Daraby, B.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.03.2016
Subjects
Analysis
Mathematics
Mathematics and Statistics
Operator Theory
Fusion frame
Upper redundancy
Primary 42C40
47A58
Lower redundancy
Erasure
Redundancy function
Secondary 41A58
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Summary:Upon improving and extending the concept of redundancy of frames, we introduce the notion of redundancy of fusion frames, which is concerned with the properties of lower and upper redundancies. These properties are achieved by considering the minimum and maximum values of the redundancy function which is defined from the unit sphere of the Hilbert space into the positive real numbers. In addition, we study the relationship between redundancy of frames (fusion frames) and dual frames (dual fusion frames). Moreover, we indicate some results about excess of fusion frames. We state the relationship between redundancy of local frames and fusion frames in a particular case. Furthermore, some examples are also given.
ISSN:1661-8254
1661-8262
DOI:10.1007/s11785-015-0489-0