Geodesic
Banach lattices with topologically full centre
Vladikavkazskij matematičeskij žurnal, Tome 11 (2009) no. 2, pp. 50-60

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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. 
@article{VMJ_2009_11_2_a7,
     author = {A. W. Wickstead},
     title = {Banach lattices with topologically full centre},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {50--60},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2009_11_2_a7/}
}
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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/