Weak and unbounded order convergence in Banach lattices
1977 ◽
Vol 24
(3)
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pp. 312-319
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Keyword(s):
AbstractA net (xy) in a vector lattice is unbounded order convergent (uo-convergent) to 0 if u ∧ |xv| order converges to 0 for all u ≧ 0. We consider, in a Banach lattice, the relationship between weak and uo-convergence. We characterise those Banach lattices in which weak convergence implies uo-convergence and those in which uo-convergence of a bounded net implies weak convergence. Finally we combine the results to characterise those Banach lattices in which weak and uo-convergence coincide for bounded nets.
1986 ◽
Vol 40
(3)
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pp. 287-298
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1974 ◽
Vol 11
(2)
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pp. 231-254
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Keyword(s):
1974 ◽
Vol 15
(1)
◽
pp. 13-13
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1993 ◽
Vol 35
(2)
◽
pp. 207-217
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Keyword(s):
1964 ◽
Vol 60
(2)
◽
pp. 205-207
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1973 ◽
Vol 18
(3)
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pp. 239-246
1997 ◽
Vol 63
(1)
◽
pp. 16-31
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Keyword(s):
1978 ◽
Vol 83
(2)
◽
pp. 269-272
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Keyword(s):
1995 ◽
Vol 37
(1)
◽
pp. 65-67
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