Results on Continuous K-frames for Quaternionic (Super) Hilbert Spaces
Abstract
This paper aims to explore the concept of continuous \( K \)-frames in quaternionic Hilbert spaces. First, we investigate \( K \)-frames in a single quaternionic Hilbert space \( H \), where \( K \) is a right H-linear bounded operator acting on \( H \). Then, we extend the research to two quaternionic Hilbert spaces, \( H1 \) and \( H2 \), and study \( K1 K2 \)-frames for the super quaternionic Hilbert space \( H1 H2 \), where \( K1 \) and \( K2 \) are right H-linear bounded operators on \( H1 \) and \( H2 \), respectively. We examine the relationship between the continuous \( K1 K2 \)-frames and the continuous \( K1 \)-frames for \( H1 \) and the continuous \( K2 \)-frames for \( H2 \). Additionally, we explore the duality between the continuous \( K1 K2 \)-frames and the continuous \( K1 \)- and \( K2 \)-frames individually.
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