Abstract
In this paper, we will prove that every derivation of completely distributive subspace lattice (CDS) algebras on Banach space is automatically continuous. This is new even in the Hilbert space case. As an application of this result, we obtain that every additive derivation of nest algebras on Banach spaces is inne. We will also prove that every isomorphism between nest algebras on Banach space is automatically continuous, and in addition, is spatial.
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