On duality of modular G-Riesz bases and G-Riesz bases in Hilbert C*-modules
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Abstract:
In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*-modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary condition for a dual of a g-Riesz basis to be again a g-Riesz basis. We nd a situation for a g-Riesz basis to have unique dual g-Riesz basis. Also, we show that every modular g-Riesz basis is a g-Riesz basis in Hilbert C*-module but the opposite implication is not true.
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Journal title
volume 04 issue 01
pages 53- 63
publication date 2015-04-01
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