Diagonalizing ''compact'' operators on Hilbert W*-modules

TL;DR

This paper proves that all self-adjoint compact operators on self-dual Hilbert modules over W*-algebras are diagonalizable, providing detailed properties of their eigenvalues and eigenvectors.

Contribution

It establishes the diagonalizability of self-adjoint compact operators on Hilbert W*-modules, a significant extension of classical operator theory.

Findings

Self-adjoint compact operators are diagonalizable on Hilbert W*-modules.

Eigenvalues and eigenvectors have specific characterized properties.

Results extend classical operator diagonalization to the setting of W*-modules.

Abstract

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