Abstract

A CDC algebra is a reflexive operator algebra whose lattice is completely distributive and commutative. Nearly twenty years ago, Gilfeather and Moore obtained a necessary and sufficient condition for an isomorphism between CDC algebras to be quasi-spatial. In this paper, we give a necessary and sufficient condition for a derivation δ of CDC algebras to be quasi-spatial. Namely, δ is quasi-spatial if and only if δ ( R ) maps the kernel of R into the range of R for each finite rank operator R. Some examples are presented to show the sharpness of the condition. We also establish a sufficient condition on the lattice that guarantees that every derivation is quasi-spatial.

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