For W*-algebras A and self-dual Hilbert A-modules M we show that every selfadjoint, ”compact” module operator on M is diagonalizable. Some specific properties of the eigenvalues and of the eigenvectors are described.

Generalizing Jones’s notion of a planar algebra, we have previously introduced an A2-planar algebra capturing the structure contained in the double complex pertaining to the subfactor for a finite SU(3) ADE graph with a flat cell system. We now introduce the notion of modules over an A2-planar algebra, and describe certain irreducible Hilbert A2-TL-modules. We construct an A2-graph planar algeb...

We describe three methods to determine the structure of (sufficiently continuous) representations of the algebra Ba(E) of all adjointable operators on a Hilbert B–module E by operators on a Hilbert C–module. While the last and latest proof is simple and direct and new even for normal representations of B(H) (H some Hilbert space), the other ones are direct generalizations of the representation ...