Continuous \(g\)-frame in Hilbert \(C^{\ast}\)-modules. (English) Zbl 1227.46039

Kouchi, Mehdi Rashidi; Nazari, Akbar

Abstr. Appl. Anal. 2011, Article ID 361595, 20 p. (2011).

Summary: We give a generalization of \(g\)-frames in Hilbert \(C^{\ast}\)-modules that was introduced by A. Khosravi and B. Khosravi [Int. J. Wavelets Multiresolut. Inf. Process. 6, No. 3, 433–446 (2008; Zbl 1153.46035)]. Then X.-C. Xiao and X.-M. Zeng [J. Math. Anal. Appl. 363, No. 2, 399–408 (2010; Zbl 1189.46050)] investigated some of its properties. This generalization is a natural generalization of continuous and discrete \(g\)-frames and frames in Hilbert space, too. We characterize continuous \(g\)-Riesz \(g\)-frames in Hilbert \(C^{\ast}\)-modules.

MSC:

46L08	\(C^*\)-modules
42C15	General harmonic expansions, frames

Citations:

Zbl 1153.46035; Zbl 1189.46050

References:

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