The stability of Banach frames in Banach spaces (Q627575)

The authors give a characterization of a Banach frame for a Banach space in terms of the pseudoinverse operator. They also study the stability of a Banach frame for a Banach space. The theorems presented generalize, and in some cases improve, results of \textit{S. J. Favier} and the reviewer [Appl. Comput. Harmon. Anal. 2, No.2, 160--173 (1995 (1995; Zbl 0829.46006)], \textit{P. Casazza} et al. [J. Math. Anal. Appl. 307, No. 2, 710--723 (2005; Zbl 1091.46007)], \textit{O. Christensen} and \textit{C. Heil} [Math. Nachr. 185, 33--47 (1997; Zbl 0868.42013)], \textit{P. K. Jain, S. K. Kaushik} et al. [Int. J. Wavelets Multiresolut. Inf. Process. 4(3), 559--565 (2006; Zbl 1213.42113)] and [Bull. Korean Math. Soc. 44, No. 1, 73--81 (2007; Zbl 1190.42013)], \textit{J. Xin} and \textit{J. Y. Zhou} [Acta Math. Sin. 45, No. 6, 1165--1170 (2002; Zbl 1113.46306)], and \textit{O. Christensen} and \textit{D. I. Stoeva} [Adv. Comput. Math 18, 117-126 (2003; Zbl 1012.42024)].