Vol. 6, No. 3, 2013

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On duals of $p$-frames

Ali Akbar Arefijamaal and Leili Mohammadkhani

Vol. 6 (2013), No. 3, 301–309
Abstract

The concept of frames in a Banach space has been introduced by Gröchenig and developed by several authors. The main feature of a frame is to present every element of the underlying Banach space as a norm-convergent series. In this decomposition, the dual frame plays an essential role. The existence of a dual p-frame is not guaranteed in general. Some characterizations of duals of p-frames are given in this paper.

Keywords
frame, Banach space, dual frame, $p$-frame, alternate dual
Mathematical Subject Classification 2010
Primary: 42C15
Secondary: 46B15
Milestones
Received: 9 May 2012
Revised: 3 October 2012
Accepted: 6 October 2012
Published: 8 September 2013

Communicated by Mohammad Sal Moslehian
Authors
Ali Akbar Arefijamaal
Department of Mathematics and Computer Sciences
Hakim Sabzevari University
Sabzevar
Iran
Leili Mohammadkhani
Department of Mathematics and Computer Sciences
Hakim Sabzevari University
Sabzevar
Iran