Functional analysis in the dual quaternion space

In this study; initially given two different complexification of real vector space in literature and some basic definitions and concepts of functional analysis is mentioned for complex quaternion vector space. In the original part of our thesis, as dualization of real vector spaces with the help of ring of dual numbers and correspondingly, quaternization of real vector space through dual quaternions are examined, module structure of dual quaternions is obtained . besides some fundamantel definitions and notations of semi-norm, semi Banach and semi Hilbert modules on this module structure of dual quaternions which is obtained in previous chapters.