DERIVATIONS AND ISOMORPHISMS OF CERTAIN REFLEXIVE OPERATOR-ALGEBRAS

In this paper, we will prove that every derivation of completely distr ibutive subspace lattice (CDS)algebras on Banach space is automaticall y continuous. This is new even in the Hilbert space case. As an applic ation of this result, we obtain that every additive derivation bf nest algebras on Banach spaces is inner. We will also prove that every iso morphism between nest algebras on Banach space is automatically contin uous, and in addition, is spatial.