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 Li1,2 and Hemant Pendharkar3

1Department of Mathematics, Hunan Normal University, Hunan, 410081, China
2Department of Mathematics, University of New Hampshire, Durham 03824, NH, USA
3Department of Mathematics and Computer Science, Elizabeth City State University, Elizabeth City 27909, NC, USA

Received 20 March 1998; Revised 2 July 1999

Copyright © 2000 Jiankui Li and Hemant Pendharkar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.