On the commutant of the ideal centre
Abstract
The centre
of a Riesz space E is the collection of all operators T on E that satisfy
for some
, where I is the identity operator. We study the commutant
of
in the order bounded operators on E. If E is a Riesz space with topologically full centre, we identify
with the orthomorphisms of E.
![Z(E)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/756207062cb827060f8d3949c607599e.png)
![-λ I≤ T≤λ I](http://siba-ese.unile.it/plugins/generic/latexRender/cache/213bbe19c99086db5613ee4070386436.png)
![λ ∈ R](http://siba-ese.unile.it/plugins/generic/latexRender/cache/750d3edcc3a40e27420bffc7fed2067d.png)
![Z(E)_C](http://siba-ese.unile.it/plugins/generic/latexRender/cache/6efeaf93ca297dd6403513f272505432.png)
![Z(E)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/756207062cb827060f8d3949c607599e.png)
![Z(E)_C](http://siba-ese.unile.it/plugins/generic/latexRender/cache/6efeaf93ca297dd6403513f272505432.png)
DOI Code:
10.1285/i15900932v18n1p63
Keywords:
Riesz space; Ideal center; Commutant; Orthomorphisms
Classification:
46A40
Full Text: PDF