The compact range property and C0
1986 ◽
Vol 28
(1)
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pp. 113-114
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The purpose of this short note is to make an observation about Dunford–Pettis operators from L1[0, 1] to C0. Recall that an operator T:E→F (where E and F are Banach spaces) is called Dunford–Pettis if T takes weakly convergent sequences of E into norm convergent sequences of F. A Banach space F has the Compact Range Property (CRP) if every operator T:L1]0, 1]→F is Dunford–Pettis. Talagrand shows in his book [2] that C0 does not have the CRP. It is of interest (especially in mathematical economics [3]) to note that every positive operator from L1[0, 1] to C0 is Dunford–Pettis.
2001 ◽
Vol 43
(1)
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pp. 125-128
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2021 ◽
Vol 2021
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pp. 1-5
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2010 ◽
Vol 82
(1)
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pp. 10-17
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2006 ◽
Vol 49
(1)
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pp. 39-52
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2005 ◽
Vol 71
(1)
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pp. 107-111
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