Spectral Analysis in non-Archimedean Hilbert Spaces.
This is joint work with T. Diagana, T.H. Miabey, F. Ramarason. We will define non-Archimedian Banach amd Hilbert Spaces. Then we solve the problem of finding the spectrum of certain operators of the form A=D+F, where D is a diagonal operator and F is an operator of finite rank in the non-Archimedean Hilbert space E sub omega. We make extensive use of the theory of Fredhom operators and the concept of essential spectrum. This is an extension of work of B. Diarra and work of T. Diagana and G.D. McNeal.