g-FRAMES AND MODULAR RIESZ BASES IN HILBERT C*-MODULES

被引：21
作者：
Khosravi, Amir [1 ]
Khosravi, Behrooz [2 ]
机构：
[1] Tarbiat Moallem Univ, Fac Math Sci & Comp, Tehran 15618, Iran
[2] Amir Kabir Univ Technol, Fac Math & Comp Sci, Dept Pure Math, Tehran Polytech, Tehran 15914, Iran
来源：
INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING | 2012年 / 10卷 / 02期
关键词：
g-frame; g-Riesz basis; modular g-Riesz basis; Hilbert C*-module; modular Riesz basis; FUSION FRAMES; SPACES;
D O I：
10.1142/S0219691312500130
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
In this paper we introduce modular Riesz basis, modular g-Riesz basis in Hilbert C*-modules in a very natural way and we show that they share many properties with Riesz basis and g-Riesz basis in Hilbert spaces. We also found that by using the fact that every finitely or countably generated Hilbert C*-module over a unital C*-algebra has a standard Parseval frame, we characterize g-frames, modular Riesz bases and modular g-Riesz bases. Finally we obtain a perturbation result for modular g-Riesz bases.
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页数：12
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