On duality of modular G-Riesz bases and G-Riesz bases in Hilbert C*-modules

Subject Areas : Functional analysis

M. Rashidi-Kouchi ¹

1 - Young Researchers and Elite Club Kahnooj Branch, Islamic Azad University, Kerman, Iran

Received: 2014-10-09 Accepted : 2015-03-02 Published : 2015-04-01

Keywords: modular g-Riesz basis, g-Riesz basis, dual g-Riesz basis, Hilbert C∗-module,

Abstract :

In this paper, we investigate duality of modular g-Riesz bases and g-Riesz basesin 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 giveng-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary conditionfor a dual of a g-Riesz basis to be again a g-Riesz basis. We find a situation for a g-Rieszbasis to have unique dual g-Riesz basis. Also, we show that every modular g-Riesz basis is ag-Riesz basis in Hilbert C*-module but the opposite implication is not true.

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