We define the concept of continuous -frames (-frames) for Banach spaces, generalizing discrete -frames. We prove that under certain conditions the direct sum of a finite number of -frames is again a -frame. We obtain equivalent conditions for duals of -Bessel mappings and show existence and uniqueness of duals of independent -frames. Lastly we discuss perturbation of these frames.
"Continuous $p$-Bessel mappings and continuous $p$-frames in Banach spaces." Involve 4 (2) 167 - 186, 2011. https://doi.org/10.2140/involve.2011.4.167