The order boundedness of band preserving operators on uniformly complete vector lattices
1985 ◽
Vol 97
(3)
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pp. 481-487
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Keyword(s):
1. Introduction. A linear operator T on a vector lattice is band preserving if x⊥ y implies Tx ⊥ y. Much is known about the order bounded band preserving operators on an Archimedean vector lattice. The collection of all of these forms an Abelian algebra under composition and a vector lattice for the operator order (see [7], [8] and [13] amongst others). Very little appears to be known about band preserving operators which are not order bounded apart from some isolated examples ([11], [13], [1] and [17]) and some non-existence results ([11] and [1]).
1981 ◽
Vol 89
(1)
◽
pp. 119-128
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1968 ◽
Vol 20
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pp. 1136-1149
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Keyword(s):
1971 ◽
Vol 12
(1)
◽
pp. 69-74
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1974 ◽
Vol 18
(1)
◽
pp. 76-77
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Keyword(s):
2010 ◽
Vol 110
(-1)
◽
pp. 83-94
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1971 ◽
Vol 5
(3)
◽
pp. 331-335
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Keyword(s):