CHARACTEIZATIONS OF WOVEN g-FRAMES AND WEAVING g-FRAMES IN HILBERT SPACES AND C*-MODULES*

doi:10.1007/s10473-023-0609-2

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (6): 2471-2482.doi: 10.1007/s10473-023-0609-2

CHARACTEIZATIONS OF WOVEN g-FRAMES AND WEAVING g-FRAMES IN HILBERT SPACES AND C^-MODULES^

Amir KHOSRAVI^†, Mohammad Reza FARMANI

Faculty of Mathematical Sciences and Computer, Kharazmi University, 599 Taleghani Ave., Tehran 15618, Iran

收稿日期:2022-06-21 修回日期:2022-10-12 发布日期:2023-12-08
通讯作者: †Amir KHOSRAVI, E-mail: khosravi_amir@yahoo.com; khosravi@khu.ac.ir
作者简介:Mohammad Reza FARMANI, E-mail: mr.farmanis@gmail.com

CHARACTEIZATIONS OF WOVEN g-FRAMES AND WEAVING g-FRAMES IN HILBERT SPACES AND C^-MODULES^

Amir KHOSRAVI^†, Mohammad Reza FARMANI

Faculty of Mathematical Sciences and Computer, Kharazmi University, 599 Taleghani Ave., Tehran 15618, Iran

Received:2022-06-21 Revised:2022-10-12 Published:2023-12-08
Contact: †Amir KHOSRAVI, E-mail: khosravi_amir@yahoo.com; khosravi@khu.ac.ir
About author:Mohammad Reza FARMANI, E-mail: mr.farmanis@gmail.com

摘要/Abstract

摘要： In this paper, using Parseval frames we generalize Sun's results to g-frames in Hilbert $C^*$-modules. Moreover, for g-frames in Hilbert spaces, we present some characterizations in terms of a family of frames, not only for orthonormal bases. Also, we have a note about a comment and a relation in the proof of Proposition 5.3 in [D. Li et al., On weaving g-frames for Hilbert spaces, Complex Analysis and Operator Theory, 2020]. Finally, we have some results for g-Riesz bases, woven and P-woven g-frames.

关键词: g-frame, fusion frame, woven frame, Riesz basis, g-Riesz basis

Abstract: In this paper, using Parseval frames we generalize Sun's results to g-frames in Hilbert $C^*$-modules. Moreover, for g-frames in Hilbert spaces, we present some characterizations in terms of a family of frames, not only for orthonormal bases. Also, we have a note about a comment and a relation in the proof of Proposition 5.3 in [D. Li et al., On weaving g-frames for Hilbert spaces, Complex Analysis and Operator Theory, 2020]. Finally, we have some results for g-Riesz bases, woven and P-woven g-frames.

Key words: g-frame, fusion frame, woven frame, Riesz basis, g-Riesz basis

中图分类号:

46L99

Amir KHOSRAVI, Mohammad Reza FARMANI. CHARACTEIZATIONS OF WOVEN g-FRAMES AND WEAVING g-FRAMES IN HILBERT SPACES AND C^*-MODULES^*[J]. 数学物理学报(英文版), 2023, 43(6): 2471-2482.

Amir KHOSRAVI, Mohammad Reza FARMANI. CHARACTEIZATIONS OF WOVEN g-FRAMES AND WEAVING g-FRAMES IN HILBERT SPACES AND C^*-MODULES^*[J]. Acta mathematica scientia,Series B, 2023, 43(6): 2471-2482.

参考文献

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CHARACTEIZATIONS OF WOVEN g-FRAMES AND WEAVING g-FRAMES IN HILBERT SPACES AND C^-MODULES^

CHARACTEIZATIONS OF WOVEN g-FRAMES AND WEAVING g-FRAMES IN HILBERT SPACES AND C^-MODULES^

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