# Order bounded derivations on Archimedean almost f -algebras

Order bounded derivations on Archimedean almost f -algebras Let A be an Archimedean f -algebra and let N(A) be the set of all nilpotent elements of A. Colville et al. [6] proved that a positive linear map D : A → A is a derivation if and only if \$\${D(A)\subset N(A)}\$\$ and D(A 2) = {0}, where A 2 is the set of all products ab in A. In this paper, we establish a result corresponding to the Colville–Davis–Keimel theorem for an order bounded derivation D on an Archimedean almost f -algebra, which generalizes the results of Boulabiar [3]. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Order bounded derivations on Archimedean almost f -algebras

, Volume 14 (2) – May 5, 2009
7 pages

/lp/springer_journal/order-bounded-derivations-on-archimedean-almost-f-algebras-xeS5Hu4OFL
Publisher
Springer Journals
Subject
Mathematics; Econometrics; Calculus of Variations and Optimal Control; Optimization; Potential Theory; Operator Theory; Fourier Analysis
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-009-0013-8
Publisher site
See Article on Publisher Site

### Abstract

Let A be an Archimedean f -algebra and let N(A) be the set of all nilpotent elements of A. Colville et al. [6] proved that a positive linear map D : A → A is a derivation if and only if \$\${D(A)\subset N(A)}\$\$ and D(A 2) = {0}, where A 2 is the set of all products ab in A. In this paper, we establish a result corresponding to the Colville–Davis–Keimel theorem for an order bounded derivation D on an Archimedean almost f -algebra, which generalizes the results of Boulabiar [3].

### Journal

PositivitySpringer Journals

Published: May 5, 2009

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