An absolute continuity for positive operators on Banach lattices.
Feldman, W., Piston, C., Piston, Calvin E. (1991)
International Journal of Mathematics and Mathematical Sciences
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Feldman, W., Piston, C., Piston, Calvin E. (1991)
International Journal of Mathematics and Mathematical Sciences
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C.D. Aliprantis, Owen Burkinshaw (1980)
Mathematische Zeitschrift
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N. Ghoussoub, W.B. Johnson (1987)
Mathematische Zeitschrift
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J. Szulga (1985)
Studia Mathematica
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Xiu-Juan Hua, Hua-Peng Zhang, Yao Ouyang (2021)
Kybernetika
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In this note, we point out that Theorem 3.1 as well as Theorem 3.5 in G. D. Çaylı and F. Karaçal (Kybernetika 53 (2017), 394-417) contains a superfluous condition. We have also generalized them by using closure (interior, resp.) operators.
Charles E. Cleaver (1972)
Colloquium Mathematicae
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Roman Drnovšek (2012)
Studia Mathematica
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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.
Wojciech Bartoszek (1990)
Annales Polonici Mathematici
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William Feldmann (1988)
Mathematische Zeitschrift
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O. Agratini (1998)
Publications de l'Institut Mathématique
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N. Ghoussoub, T. Figiel, W.B. Johnson (1981)
Mathematische Annalen
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Julio Flores, Pedro Tradacete (2008)
Studia Mathematica
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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.
Teresa Alvarez (1988)
Publicacions Matemàtiques
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In this paper we show that a Rosenthal operator factors through a Banach space containing no isomorphs of l.