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Zeitschrift für Analysis und ihre Anwendungen


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Volume 14, Issue 1, 1995, pp. 33–41
DOI: 10.4171/ZAA/661

Published online: 1995-03-31

Diagonalizing 'Compact' Operators on Hilbert W*-Modules

Michael Frank[1] and V.M. Manuilov[2]

(1) Hochschule für Technik, Wirtschaft und Kultur, Leipzig, Germany
(2) Moscow State University, Russian Federation

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.

Keywords: Diagonolization of 'compact' operators, Hubert W*-modules, W*-algebras, eigenvalues, eigenvectors

Frank Michael, Manuilov V.M.: Diagonalizing 'Compact' Operators on Hilbert W*-Modules. Z. Anal. Anwend. 14 (1995), 33-41. doi: 10.4171/ZAA/661