S-spectrum and associated continuous frames on quaternionic Hilbert spaces

Abstract

As needed for the construction of rank $n$ 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 {\em Ann.Phys.}, {\bf 222} (1993), 1-37., various classes of rank $n$ continuous frames and their equivalencies on a right quaternionic Hilbert space are presented.