Banach lattices with topologically full centre
Автор: Wickstead Anthony W.
Журнал: Владикавказский математический журнал @vmj-ru
Статья в выпуске: 2 т.11, 2009 года.
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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.
Короткий адрес: https://sciup.org/14318274
IDR: 14318274
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