@article{Zhang2026, 
author = {Jianping Zhang and Kepu Li},
title = {Characterizations and constructions of tight    K-frames in quaternionic Hilbert spaces},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {7},
pages = {22943-22958},
keywords = {quaternionic Hilbert space, tight frame, K-frame, tight K-frame, Parseval K-frame},
url = {https://www.sciopen.com/article/10.3934/math.2026924},
doi = {10.3934/math.2026924},
abstract = {This paper introduces the notion of tight    K-frames in quaternionic Hilbert spaces and investigates their characterizations and constructions. By employing analysis and frame operators, we provide an operator-theoretic characterization and demonstrate that a tight    K-frame with bound        C    1   reduces to an ordinary tight frame with bound        C    2   if and only if        C    1    K      K    ∗    =      C    2        I                  H            . Several construction methods are presented, including operator actions and combinations of Bessel sequences, with refined results for Parseval    K-frames. Moreover, we establish a bijection between tight    K-frames and classical tight frames on the subspace        Ran    (      K    ∗    ), showing that each can be obtained from the other via the pseudo-inverse of    K.}
}