An absolute continuity for positive operators on Banach lattices.

Feldman, W.; Piston, C.; Piston, Calvin E.

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Factoring Operators Through Banach Lattices Not Containing C(0, 1).

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Factorization and domination of positive Banach-Saks operators

Julio Flores, Pedro Tradacete (2008)

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It is proved that every positive Banach-Saks operator T: E → F between Banach lattices E and F factors through a Banach lattice with the Banach-Saks property, provided that F has order continuous norm. By means of an example we show that this order continuity condition cannot be removed. In addition, some domination results, in the Dodds-Fremlin sense, are obtained for the class of Banach-Saks operators.

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Once more on positive commutators

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Let A and B be bounded operators on a Banach lattice E such that the commutator C = AB - BA and the product BA are positive operators. If the product AB is a power-compact operator, then C is a quasi-nilpotent operator having a triangularizing chain of closed ideals of E. This answers an open question posed by Bračič et al. [Positivity 14 (2010)], where the study of positive commutators of positive operators was initiated.