Duals and approximate duals of von Neumann-Schatten \(p\)-frames
The notion of von Neumann-Schatten \(p\)-frames introduced in [\textit{G. Sadeghi} and \textit{A. Arefijamaal}, Mediterr. J. Math. 9, No. 3, 525--535 (2012; Zbl 1266.46010)] combines the features of \(p\)-frames from [\textit{O. Christensen} and \textit{D. T. Stoeva}, Adv. Comput. Math. 18, No. 2--4, 117--126 (2003; Zbl 1012.42024)] and \(g\)-frames from [\textit{W. Sun}, J. Math. Anal. Appl. 322, No. 1, 437--452 (2006; Zbl 1129.42017)]. In this paper, the authors characterize the existence of dual von Neumann-Schatten \(p\)-frames in terms of the complementability of a certain subspace. They also provide a natural extension of the idea of approximately dual frames pioneered by \textit{O. Christensen} and \textit{R. S. Laugesen} [Sampl. Theory Signal Image Process. 9, No. 1--3, 77--89 (2010; Zbl 1228.42031)] and a stability result for such dual frames under additive perturbations.
scientific article; zbMATH DE number 7626526
scientific article