Weighted and Controlled Continuous g-Frames and their Multipliers in Hilbert Spaces

Year 2016, Volume: 13 Issue: 1, - , 01.05.2016

Sayyed Mehrab Ramezani Akbar Nazari

Abstract

A generalization of weighted, multiplier, controlled from frame and Bessel sequences to continuous
g-frames and continuous g-Bessel sequences in Hilbert spaces is presented in this study. Moreover,
we find a dual of a continuous g-frame in the case that the multiplier operator is invertible. Finally, it is
demonstrated that a controlled continuous g-frame is equivalent to a continuous g-frame.

Keywords

Continuous g-frame, continuous g-multiplier, weighted continuous g-frame

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