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LOCAL DERIVATIONS AND LOCAL AUTOMORPHISMS ON SOME ALGEBRAS

DON HADWIN and JIANKUI LI
Journal of Operator Theory
Vol. 60, No. 1 (Summer 2008), pp. 29-44
Published by: Theta Foundation
Stable URL: http://www.jstor.org/stable/24715835
Page Count: 16
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LOCAL DERIVATIONS AND LOCAL AUTOMORPHISMS ON SOME ALGEBRAS
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Abstract

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 𝓛 is a commutative subspace lattice and π“œ is a unital Banach alg𝓛-bimodule, then every bounded local derivation from alg𝓛 into π“œ is a derivation and that if π’œ is a nest subalgebra in a factor von Neumann algebra π“œ, then every local derivation from π’œ into π“œ is a derivation.

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