On K-frame generators for unitary systems in Hilbert C∗-modules

In this paper, we first provide an necessary and sufficient condition for vectors to be K -frame generators for unitary systems in Hilbert C ∗ -modules. We then characterize the K -dual Bessel generators of K -frame generators for unitary systems in Hilbert C ∗ -modules from several aspects. We also...

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Bibliographic Details
Published inJournal of pseudo-differential operators and applications Vol. 12; no. 1
Main Author Xiang, Zhong-Qi
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.03.2021
Springer Nature B.V
Subjects
Algebra
Analysis
Applications of Mathematics
Functional Analysis
Generators
Hilbert space
Mathematics
Mathematics and Statistics
Modules
Operator Theory
Partial Differential Equations
dual Bessel generator
46L08
47B48
module
frame generator
Hilbert
42C15
46H25
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Summary:In this paper, we first provide an necessary and sufficient condition for vectors to be K -frame generators for unitary systems in Hilbert C ∗ -modules. We then characterize the K -dual Bessel generators of K -frame generators for unitary systems in Hilbert C ∗ -modules from several aspects. We also examine the properties of K -frame generators for unitary systems in Hilbert C ∗ -modules under adjointable operators, and some methods to construct new K -frame generators from given ones are presented. The results we obtained improve one corresponding result in Hilbert spaces setting and reflect, to a certain extent, the different behaviors of K -frame generators for unitary systems shown respectively in Hilbert C ∗ -modules and Hilbert spaces.
ISSN:1662-9981
1662-999X
DOI:10.1007/s11868-021-00377-z