Frame Multipliers for discrete frames on Quaternionic Hilbert Spaces

TL;DR

This paper extends the theory of discrete frames and frame multipliers to quaternionic Hilbert spaces, exploring their properties and relationships in a non-commutative setting.

Contribution

It introduces the concept of controlled frames and investigates their equivalence to usual frames in quaternionic Hilbert spaces, also analyzing frame multipliers and weighted frames.

Findings

Controlled frames are equivalent to usual frames under certain conditions

Established connections between frame multipliers and weighted frames

Extended frame theory to non-commutative quaternionic setting

Abstract

In this note, following the complex theory, we examine discrete controlled frames, discrete weighted frames and frame multipliers in a non-commutative 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.