Pseudosymmetric Spaces as Generalization of Symmetric spaces

In this paper, the concept of a pseudosymmetric space which is a natural generalization of the concept of a symmetric space is defined. All basic concepts such as the Luxemburg representa-tion theorem, the Boyd indices, the fundamental function and its properties, Calderon's theorem, etc., is transferred over the pseu-dosymmetric case. Examples are given for pseudosymmetric spaces. The quasi-symmetric spaces expand the scope of the application of symmetric space results.