Some properties of \(K\)-frames in quaternionic Hilbert spaces (Q2302306)

In the present paper, the author considers \(K\)-frames in quaternionic Hilbert spaces. At first, some concepts and results about the algebra of quaternions, right quaternionic Hilbert spaces, operators on right quaternionic Hilbert spaces, frames and \(K\)-frames in right quaternionic Hilbert spaces are stated. Then, some properties of \(K\)-frames in right quaternionic Hilbert spaces are obtained, especially the invertibility of the \(K\)-frame operators is discussed and the construction of \(K\)-frames is considered. Moreover, the stability of \(K\)-frames under perturbations is studied.