Advances in Operator Theory

A note on O-frames for operators

Chander Shekhar and Shiv Kumar Kaushik

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Abstract

A sufficient condition for a boundedly complete O-frame and a necessary condition for an unconditional O-frame are given. Also, a necessary and sufficient condition for an absolute O-frame is obtained. Finally, it is proved that if two operators have an absolute O-frame, then their product also has an absolute O-frame.

Article information

Source
Adv. Oper. Theory, Volume 2, Number 3 (2017), 383-395.

Dates
Received: 18 February 2017
Accepted: 4 June 2017
First available in Project Euclid: 4 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.aot/1512431682

Digital Object Identifier
doi:10.22034/aot.1702-1122

Mathematical Reviews number (MathSciNet)
MR3730060

Zentralblatt MATH identifier
1372.42031

Subjects
Primary: 42C15: General harmonic expansions, frames
Secondary: 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type

Keywords
Schauder frame O-frame Unconditional O-frame

Citation

Shekhar, Chander; Kaushik, Shiv Kumar. A note on O-frames for operators. Adv. Oper. Theory 2 (2017), no. 3, 383--395. doi:10.22034/aot.1702-1122. https://projecteuclid.org/euclid.aot/1512431682


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