Derivations and isomorphisms of certain reflexive operator algebras
Copyright policy )Derivations and isomorphisms of certain reflexive operator algebras
Summary: We 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 inner. We also prove that every isomorphism between nest algebras on Banach space is automatically continuous, and in addition, is spatial.
- Qufu Normal University China (People's Republic of)
- Fudan University China (People's Republic of)
- Qufu Normal University China (People's Republic of)
Abstract operator algebras on Hilbert spaces, derivation of completely distributive subspace lattice algebras, Commutators, derivations, elementary operators, etc., Linear spaces of operators, CDS algebra, nest algebras, Automatic continuity
Abstract operator algebras on Hilbert spaces, derivation of completely distributive subspace lattice algebras, Commutators, derivations, elementary operators, etc., Linear spaces of operators, CDS algebra, nest algebras, Automatic continuity
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