Duals of a frame in quaternionic Hilbert spaces
SK Sharma, G Singh, S Sahu - arXiv preprint arXiv:1803.05773, 2018 - arxiv.org
SK Sharma, G Singh, S Sahu
arXiv preprint arXiv:1803.05773, 2018•arxiv.orgFrames in a separable quaternionic Hilbert space were introduced and studied in [17] to
have more applications. In this paper, we extend the study of frames in quaternionic Hilbert
spaces and introduce different types of duals of a frame in separable quaternionic Hilbert
spaces. As an application, we give the orthogonal projection of $\ell^ 2 (\HH) $ onto the
range of analysis operator of the given frame, in terms of elements of canonical dual frame
and elements of the frame in quaternionic Hilbert space. Finally, we give an expression for …
have more applications. In this paper, we extend the study of frames in quaternionic Hilbert
spaces and introduce different types of duals of a frame in separable quaternionic Hilbert
spaces. As an application, we give the orthogonal projection of $\ell^ 2 (\HH) $ onto the
range of analysis operator of the given frame, in terms of elements of canonical dual frame
and elements of the frame in quaternionic Hilbert space. Finally, we give an expression for …
Frames in a separable quaternionic Hilbert space were introduced and studied in [17] to have more applications. In this paper, we extend the study of frames in quaternionic Hilbert spaces and introduce different types of duals of a frame in separable quaternionic Hilbert spaces. As an application, we give the orthogonal projection of $\ell^2(\HH)$ onto the range of analysis operator of the given frame, in terms of elements of canonical dual frame and elements of the frame in quaternionic Hilbert space. Finally, we give an expression for the orthogonal projection in terms of operators related to the frame and its canonical dual frame in quaternionic Hilbert space.
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