Frame Multipliers for Discrete Frames on Quaternionic Hilbert Spaces

Abstract

In this note, following the complex theory, we examine discrete controlled frames, discrete weighted frames and frame multipliers in a noncommutative setting, namely in a left quaternionic Hilbert space. In particular, we show that the controlled frames are equivalent to usual frames under certain conditions. We also study connection between frame multipliers and weighted frames in the same Hilbert space.