Continuous p-Bessel mappings and continuous p-frames in Banach spaces

Faroughi, Mohammad; Osgooei, Elnaz

doi:10.2140/involve.2011.4.167

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-4184 (online)

ISSN 1944-4176 (print)

Author index

To appear

Other MSP journals

Continuous $p$-Bessel mappings and continuous $p$-frames in Banach spaces

Mohammad Hasan Faroughi and Elnaz Osgooei

Vol. 4 (2011), No. 2, 167–186

DOI: 10.2140/involve.2011.4.167

Abstract

We define the concept of continuous $p$ -frames ( $c p$ -frames) for Banach spaces, generalizing discrete $p$ -frames. We prove that under certain conditions the direct sum of a finite number of $c p$ -frames is again a $c p$ -frame. We obtain equivalent conditions for duals of $c p$ -Bessel mappings and show existence and uniqueness of duals of independent $c p$ -frames. Lastly we discuss perturbation of these frames.

Keywords

frames, continuous $p$-frames, Schauder basis, reflexive space

Mathematical Subject Classification 2010

Primary: 42C99, 42C15

Secondary: 42C40

Milestones

Received: 17 February 2011

Accepted: 26 February 2011

Published: 17 January 2012

Communicated by David R. Larson

Authors

Mohammad Hasan Faroughi
Faculty of Mathematical Science University of Tabriz 29 Bahman Boulevard Tabriz Iran	Department of Mathematics Islamic Azad University, Shabestar Branch Shabestar 0098 Iran

Elnaz Osgooei
Faculty of Mathematical Science University of Tabriz 29 Bahman Boulevard Tabriz 0098 Iran

Vol. 4, No. 2, 2011