On notion of asymptotic derivations
- Authors
- Heo, Jaeseong
- Issue Date
- Feb-2012
- Publisher
- WILEY-BLACKWELL
- Keywords
- Derivations; one-parameter group of automorphisms; asymptotic derivations; Jordan derivation; MSC (2010) Primary: 46L57; Secondary: 47D03
- Citation
- MATHEMATISCHE NACHRICHTEN, v.285, no.2-3, pp.252 - 264
- Indexed
- SCIE
SCOPUS
- Journal Title
- MATHEMATISCHE NACHRICHTEN
- Volume
- 285
- Number
- 2-3
- Start Page
- 252
- End Page
- 264
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/166355
- DOI
- 10.1002/mana.201010003
- ISSN
- 0025-584X
- 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.
- Files in This Item
-
Go to Link
- Appears in
Collections - 서울 자연과학대학 > 서울 수학과 > 1. Journal Articles
![qrcode](https://api.qrserver.com/v1/create-qr-code/?size=55x55&data=https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/166355)
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.