Journal of Operator Theory

Volume 60, Issue 1, Summer 2008 pp. 29-44.

Local derivations and local automorphisms on some algebras

Authors: Don Hadwin (1) and Jiankui Li (2)
Author institution: (1) Department of Mathematics, University of New Hampshire, Durham, NH 03824, USA
(2) Department of Mathematics, East China University of Science and Technology, Shanghai 200237, P.R. China

Summary: In this paper, we study some algebras that can be generated, as algebras, by their idempotents and discuss local derivations and local automorphisms on these algebras. We prove that if $\mathcal L$ is a commutative subspace lattice and $\mathcal M$ is a unital Banach $\mathrm{alg} \mathcal L$-bimodule, then every bounded local derivation from $\mathrm{alg} \mathcal L$ into $\mathcal M$ is a derivation and that if $\mathcal A$ is a nest subalgebra in a factor von Neumann algebra $\mathcal M$, then every local derivation from $\mathcal A$ into $\mathcal M$ is a derivation.

Keywords: Commutative subspace lattice, derivation, idempotent, local automorphism, local derivation

Contents Full-Text PDF