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_1KK^* = C_2I_{\mathcal 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 $ {\operatorname{Ran}}(K^*) $, showing that each can be obtained from the other via the pseudo-inverse of $ K $.
Citation: Jianping Zhang, Kepu Li. Characterizations and constructions of tight $ K $-frames in quaternionic Hilbert spaces[J]. AIMS Mathematics, 2026, 11(7): 22943-22958. doi: 10.3934/math.2026924
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_1KK^* = C_2I_{\mathcal 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 $ {\operatorname{Ran}}(K^*) $, showing that each can be obtained from the other via the pseudo-inverse of $ K $.
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Jianping Zhang, Kepu Li. Characterizations and constructions of tight $ K $-frames in quaternionic Hilbert spaces[J]. AIMS Mathematics, 2026, 11(7): 22943-22958. doi: 10.3934/math.2026924
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