Spectral Theorem for a bounded self adjoint operator on a Bicomplex Hilbert space

Abstract

In this paper, we shall consider the notion of bicomplex inner product and define bicomplex Hilbert space. We shall define $L^2[a,b]$ where the functions take bicomplex values. We shall prove the Theorem for a bounded self adjoint operator on a bicomplex Hilbert space which is not compact.