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On notion of asymptotic derivations

✍ Scribed by Jaeseong Heo

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
178 KB
Volume
285
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

In this paper we introduce some notion of asymptotic derivations of a C*‐ and W*‐dynamical systems which naturally arises from a one‐parameter group of automorphisms. We show that an asymptotic derivation on a unital simple C*‐algebra or a von Neumann algebra is asymptotically inner. Every asymptotic derivation on finite dimensional C*‐algebras is induced by an inner derivation. We prove that any asymptotic derivation on commutative von Neumann algebras have a strong limit zero. An asymptotic derivation on the hyperfinite II~1~‐factor given by some one‐parameter group of automorphisms can be induced by a (inner) derivation. Finally, we show that every asymptotic Jordan derivation of a C*‐dynamical system is an asymptotic derivation and is also induced by a derivation if there exists a limit.

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