Idempotent vector spaces and their linear transformations (Q6617581)

The basic setting of this paper is linear analysis over bicomplex numbers. It introduces the notion of algebraically idempotent vector spaces -- a generalization of standard vector spaces. The results include bicomplex Jordan forms and a description of its bicomplex invariant subspace lattice diagrams. The paper also discusses bicomplex Banach and Hilbert spaces. Special emphasis has been given to the study of compact operators on bicomplex Banach spaces.