S-spectrum and associated continuous frames on quaternionic Hilbert spaces

As needed for the construction of rank nn continuous frames on a right quaternionic Hilbert space the so-called S-spectrum of a right quaternionic operator is studied. Using the S-spectrum, as for the case of complex Hilbert spaces, along the lines of the arguments of Ali et al. (1993), various classes of rank nn continuous frames and their equivalencies on a right quaternionic Hilbert space are presented.