#### Vol. 4, No. 2, 2011

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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
##### Abstract

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