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We first show that a derivation studied recently by E. Christensen has a set of analytic elements which is strong operator topology-dense in the algebra of bounded operators on a Hilbert space, which strengthens a result of Christensen. Our second main result shows that this derivation has kernel stabilization, that is, no elements have derivative eventually equal to 0 unless their first derivative is 0. As applications, we (1) show that a family of derivations on C*-algebras studied by Bratteli and Robinson has kernel stabilization, and (2) we provide sufficient conditions for when two operators which satisfy the Heisenberg Commutation Relation must both be unbounded. |
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