Continuous \(g\)-frame in Hilbert \(C^{\ast}\)-modules (Q535958)

Summary: We give a generalization of \(g\)-frames in Hilbert \(C^{\ast}\)-modules that was introduced by \textit{A. Khosravi} and \textit{B. Khosravi} [Int. J. Wavelets Multiresolut. Inf. Process. 6, No.~3, 433--446 (2008; Zbl 1153.46035)]. Then \textit{X.-C. Xiao} and \textit{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.