Dual and canonical dual of controlled K-g-frames in Hilbert spaces

Abstract

This paper is devoted to studying the controlled dual K-g-Bessel sequences of controlled K-g-frames. In fact,we introduce the concept of dual K-g-Bessel sequences of controlled K-g-frames and then, we present some necessaryand/or sufficient conditions under which a controlled g-Bessel sequence is a controlled dual K-g-frame of a given controlledK-g-frame. Subsequently, we pay attention to investigating the structure of the canonical controlled dual K-g-Besselsequence of a Parseval controlled K-g-frame and some other related results.