Some Results Concerning Riesz Bases and Frames in Banach Spaces

Authors

  • Khole Timothy Poumai
  • Shiv. K. Kaushik

Keywords:

Frames, Ed-Riesz bases, Ed-frames, Atomic systems.

Abstract

In this paper, we give characterizations of Riesz bases and near Riesz bases in Banach spaces. The notion of atomic system is defined and a characterization of atomic system has been given. Also results exhibiting relationship between frames, atomic systems and Riesz bases have been proved. Further, we show that every atomic system is a projection of a Riesz basis in Banach spaces. Finally, we give some duality results of an atomic system for Banach spaces.

Key words and phrases. Frames, Ed-Riesz bases, Ed-frames, Atomic systems.

1991 Mathematics Subject Classification. 42C15, 42C30, 42C05, 46B15

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Published

2025-05-18

How to Cite

Khole Timothy Poumai, & Shiv. K. Kaushik. (2025). Some Results Concerning Riesz Bases and Frames in Banach Spaces. Jordan Journal of Mathematics and Statistics, 10(1), 11–32. Retrieved from https://jjms.yu.edu.jo/index.php/jjms/article/view/1010

Issue

Vol. 10 No. 1 (2017)

Section

Articles