ON DUALITY OF MODULAR G-RIESZ BASES AND G-RIESZ BASES IN HILBERT C*-MODULES

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RASHIDI KOUCHI M.

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Journal Paper

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Journal: Journal of Linear and Topological Algebra Year:2015 | Volume:4 | Issue:1 Page(s): 53-63

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Title

ON DUALITY OF MODULAR G-RIESZ BASES AND G-RIESZ BASES IN HILBERT C*-MODULES

Author(s)

RASHIDI KOUCHI M. | Issue Writer Certificate

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 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 find 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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References

G-FRAMES AND THEIR DUALS FOR HILBERT C*-MODULES

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APA: Copy

RASHIDI KOUCHI, M.. (2015). ON DUALITY OF MODULAR G-RIESZ BASES AND G-RIESZ BASES IN HILBERT C*-MODULES. JOURNAL OF LINEAR AND TOPOLOGICAL ALGEBRA, 4(1), 53-63. SID. https://sid.ir/paper/335617/en

Vancouver: Copy

RASHIDI KOUCHI M.. ON DUALITY OF MODULAR G-RIESZ BASES AND G-RIESZ BASES IN HILBERT C*-MODULES. JOURNAL OF LINEAR AND TOPOLOGICAL ALGEBRA[Internet]. 2015;4(1):53-63. Available from: https://sid.ir/paper/335617/en

IEEE: Copy

M. RASHIDI KOUCHI, “ON DUALITY OF MODULAR G-RIESZ BASES AND G-RIESZ BASES IN HILBERT C*-MODULES,” JOURNAL OF LINEAR AND TOPOLOGICAL ALGEBRA, vol. 4, no. 1, pp. 53–63, 2015, [Online]. Available: https://sid.ir/paper/335617/en

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