International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 748159, 6 pages
doi:10.1155/2011/748159
Research Article

Generalized Derivations and Bilocal Jordan Derivations of Nest Algebras

1College of Mathematics and Physics, Chongqing University of Post and Telecom, Chongqing 400086, China
2College of Communication Engineering, Chongqing University, Chongqing 400044, China

Received 19 December 2010; Accepted 13 January 2011

Academic Editor: Jianming Zhan

Copyright © 2011 Dangui Yan and Chengchang Zhang. 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 𝐻 be a complex Hilbert space and 𝐵 ( 𝐻 ) the collection of all linear bounded operators, 𝔄 is the closed subspace lattice including 0 an 𝐻 , then 𝔄 is a nest, accordingly alg 𝔄 = { 𝑇 𝐵 ( 𝐻 ) 𝑇 𝑁 𝑁 , 𝑁 𝔄 } is a nest algebra. It will be shown that of nest algebra, generalized derivations are generalized inner derivations, and bilocal Jordan derivations are inner derivations.