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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