Characterizing R-duality in Banach spaces
In [J. Fourier Anal. Appl. 10, No. 4, 383--408 (2004; Zbl 1058.42020)], \textit{P. G. Casazza} et al. introduced the notion of Riesz-dual (R-dual) of some sequences in Hilbert spaces. They also gave some interesting properties of R-dual sequences as an attempt to generalize the duality principle from Gabor analysis to general frames in Hilbert spaces. In [J. Fourier Anal. Appl. 17, No. 4, 640--655 (2011; Zbl 1222.42031)], the first author et al. gave new characterizations of R-duality in Hilbert spaces and several examples. On the other hand, the two last authors [Acta Math. Sci., Ser. A, Chin. Ed., 29, No. 1, 94--102 (2009; Zbl 1199.42137)] extended R-duality to Banach spaces. In the present paper, the authors give some new characterizations of R-dual sequences in Banach spaces.
scientific article; zbMATH DE number 6146288