Kernel Stabilization of Unbounded Derivations on C*-algebras

Lara Ismert

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arXiv · 1808.00614

Kernel Stabilization of Unbounded Derivations on C*-algebras

Lara Ismert

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Abstract

A derivation $\delta$ on a $C^*$-algebra has kernel stabilization if for all $n\in \mathbb{N}$, $\ker \delta^n=\ker \delta.$ Our main result shows that a weakly-defined derivation studied recently by E. Christensen has kernel stabilization. As corollaries, we (1) show that a family of $*$-derivations on $C^*$-algebras studied by Bratteli and Robinson has kernel stabilization and (2) provide sufficient conditions for when operators satisfying the Heisenberg Commutation Relation must both be unbounded.

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Lara Ismert. 2018-08-02. Kernel Stabilization of Unbounded Derivations on C*-algebras. https://arxiv.org/abs/1808.00614

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