Diagonalizing 'Compact' Operators on Hilbert W*-Modules

Abstract

For W*-algebras $A$ and self-dual Hilbert $A$-modules $\mathcal{M}$ we show that every self-adjoint, "compact" module operator on $\mathcal{M}$ is diagonalizable. Some specific properties of the eigenvalues and of the eigenvectors are described.