Geodesic
Banach lattices with topologically full centre
Vladikavkazskij matematičeskij žurnal, Tome 11 (2009) no. 2, pp. 50-60 Cet article a éte moissonné depuis la source Math-Net.Ru

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After some general background discussion on the notion of a topologically full centre in a Banach lattice, we study two problems in which it has featured. In 1988 Orhon showed that if the centre is topologically full then it is also a maximal abelian algebra of bounded operators and asked if the converse is true. We give a short proof of his result and a counterexample to the converse. After noting that every non scalar central operator has a hyperinvariant band, we show that any hyperinvariant subspace must be an order ideal, provided the centre is topologically full and conclude with a counterexample to this in a general vector lattice setting. 
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A. W. Wickstead. Banach lattices with topologically full centre. Vladikavkazskij matematičeskij žurnal, Tome 11 (2009) no. 2, pp. 50-60. http://geodesic.mathdoc.fr/item/VMJ_2009_11_2_a7/

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