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.

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