A note on the stability of \(g\)-frames in Hilbert \(C^*\)-modules (Q2818338)
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scientific article; zbMATH DE number 6624825
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the stability of \(g\)-frames in Hilbert \(C^*\)-modules |
scientific article; zbMATH DE number 6624825 |
Statements
7 September 2016
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Hilbert \(C^*\)-module
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\(g\)-frame
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stability
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A note on the stability of \(g\)-frames in Hilbert \(C^*\)-modules (English)
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The author presents an equivalent definition of \(g\)-frames in Hilbert \(C^*\)-modules using the norm. Obviously, it is easier to compare the norms of two elements than to compare two (positive) elements in \(C^*\)-algebras. As an application, the author gives a complete proof of the stability of \(g\)-frames in Hilbert \(C^*\)-modules obtained by \textit{M. Rashidi-Kouchi} et al. [Int. J. Wavelets Multiresolut. Inf. Process. 12, No. 6, Article ID 1450036, 16 p. (2014; Zbl 1317.42029)] whose proof lacks the part of the lower bound inequality.
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