Derivations of certain operator algebras

Abstract

Let 𝒩 be a nest and let 𝒜 be a subalgebra of L(H) containing all rank one operators of alg 𝒩. We give several conditions under which any derivation δ from 𝒜 into L(H) must be inner. The conditions include (1) H−≠H, (2) 0+≠0, (3) there is a nontrivial projection in 𝒩 which is in 𝒜, and (4) δ is norm continuous. We also give some pplications.

Keywords

• Derivation
• nest algebra
• triangular operator algebra..