Quaternionic Banach and Hilbert Spaces

The present chapter deals with various aspects of quaternionic functional analysis and in particular supplements our previous works (Alpay et al., Recent Advances in Inverse Scattering, Schur Analysis and Stochastic Processes. Operator Theory: Advances and Applications, vol. 244, pp. 33–65. Birkhäuser, Basel, 2015, §3; Slice Hyperholomorphic Schur Analysis. Operator Theory: Advances and Applications, vol. 256. Birkhäuser/Springer, Basel, 2016), where we surveyed the main aspects of quaternionic locally convex topological right-vector spaces and where we presented some results on quaternionic functional analysis needed to study Hilbert, Pontryagin and Krein spaces of slice hyperholomorphic functions.