Year: 2017
Analysis in Theory and Applications, Vol. 33 (2017), Iss. 2 : pp. 157–177
Abstract
In this paper we study operator valued bases on Hilbert spaces and similar to Schauder bases theory we introduce characterizations of this generalized bases in Hilbert spaces. We redefine the dual basis associated with a generalized basis and prove that the operators of a dual $g$-basis are continuous. Finally we consider the stability of $g$-bases under small perturbations. We generalize two results of Krein-Milman-Rutman and Paley-Wiener [7] to the situation of $g$-basis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2017.v33.n2.6
Analysis in Theory and Applications, Vol. 33 (2017), Iss. 2 : pp. 157–177
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: $g$-bases dual $g$-bases $g$-biorthogonal sequence.