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Journal of Operator Theory

Volume 33, Issue 1, Winter 1995  pp. 117-158.

Characterization of Jordan elements in $\Psi*$-algebras

Authors Kai Lorentz
Author institution: Fachbereich Mathematik, Johannes Gutenberg Universitaet, 55099 Mainz, Germany and Universidad del Norte, Departamento de Matematicas, Barranquilla, Colombia (South America)

Summary:  We show that, given a $\Psi*$-algebra $\mathcal A \subseteq L(H)$, H a Hilbert space, and an operator $J \in \mathcal A$ which is a Jordan operator of L(H), then J also admits a Jordan decomposition within $mathcal A$. The constructive proof of this fact indicates that the structure of the projections of a $\Psi*$-algebra is very rich. We use this construction of obtain local similarity cross sections for Jordan elements $J \in \mathcal A$ within the $\Psi*$-algebra $\mathcal A$.

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