Volume 33, Issue 2
New Characterizations of Operator-Valued Bases on Hilbert Spaces
10.4208/ata.2017.v33.n2.6

Anal. Theory Appl., 33 (2017), pp. 157-177

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• Abstract

In this paper we study operator valued bases on Hilbert spaces and similar to Schauderbases theory we introduce characterizations of this generalized bases in Hilbert spaces.We redefine the dual basis associated with a generalized basis and prove that theoperators of a dual g-basis are continuous. Finally we consider the stability of g-basesunder small perturbations. We generalize two results of Krein-Milman-Rutman andPaley-Wiener [7] to the situation of $g$-basis.

• History

Published online: 2017-05

• Keywords