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On notion of asymptotic derivations

Title
On notion of asymptotic derivations
Author
허재성
Keywords
Derivations; one-parameter group of automorphisms; asymptotic derivations; Jordan derivation; MSC (2010) Primary: 46L57; Secondary: 47D03
Issue Date
2012-02
Publisher
Wiley-Blackwell
Citation
Mathematische Nachrichten, 2012, 285(2-3), P.252-264
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 II1-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.
URI
http://onlinelibrary.wiley.com/doi/10.1002/mana.201010003/abstract
ISSN
0025-584X
DOI
10.1002/mana.201010003
Appears in Collections:
COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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