Dynamical Systems on Hilbert C*-Modules

Details Dynamical Systems on Hilbert C*-Modules Dynamical Systems on Hilbert C*-Modules

2005-03-26

arxiv.org/abs/math/0503615v2

Bull. Iranian Math. Soc. 31 (2005), no. 1, 25-35

Mathematics

Operator Algebras

7 pages, minor changes, to appear in Bull. Iranian Math. Soc

Scientific paper

We investigate the generalized derivations and show that every generalized derivation on a simple Hilbert $C^*$-module either is closable or has a dense range. We also describe dynamical systems on a full Hilbert $C^*$-module ${\mathcal M}$ over a $C^*$-algebra ${\mathcal A}$ as a one-parameter group of unitaries on ${\mathcal M}$ and prove that if $\alpha: \R\to U({\mathcal M})$ is a dynamical system, where $U({\mathcal M})$ denotes the set of all unitary operator on ${\mathcal M}$, then we can correspond a $C^*$-dynamical system $\alpha^{'}$ on ${\mathcal A}$ such that if $\delta$ and $d$ are the infinitesimal generators of $\alpha$ and $\alpha^{'}$ respectively, then $\delta$ is a $d$-derivation.

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