International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 5, Pages 345-349
doi:10.1155/S0161171200003628
Derivations of certain operator algebras
Jiankui Li1
and Hemant Pendharkar2
1Department of Mathematics, Hunan Normal University, Hunan, 410081, China
2Department of Mathematics and Computer Science, Elizabeth City State University, Elizabeth City 27909, NC, USA
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.