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

Mohammad Hasan Faroughi and Elnaz Osgooei

Vol. 4 (2011), No. 2, 167–186

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.

frames, continuous $p$-frames, Schauder basis, reflexive space
Mathematical Subject Classification 2010
Primary: 42C99, 42C15
Secondary: 42C40
Received: 17 February 2011
Accepted: 26 February 2011
Published: 17 January 2012

Communicated by David R. Larson
Mohammad Hasan Faroughi
Faculty of Mathematical Science
University of Tabriz
29 Bahman Boulevard
Department of Mathematics
Islamic Azad University, Shabestar Branch
Shabestar 0098
Elnaz Osgooei
Faculty of Mathematical Science
University of Tabriz
29 Bahman Boulevard
Tabriz 0098