A Note on the Topological Group c0
Keyword(s):
A well-known result of Ferri and Galindo asserts that the topological group c 0 is not reflexively representable and the algebra WAP ( c 0 ) of weakly almost periodic functions does not separate points and closed subsets. However, it is unknown if the same remains true for a larger important algebra Tame ( c 0 ) of tame functions. Respectively, it is an open question if c 0 is representable on a Rosenthal Banach space. In the present work we show that Tame ( c 0 ) is small in a sense that the unit sphere S and 2 S cannot be separated by a tame function f ∈ Tame ( c 0 ) . As an application we show that the Gromov’s compactification of c 0 is not a semigroup compactification. We discuss some questions.
1990 ◽
Vol 100
(1)
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pp. 25-36
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1991 ◽
Vol s3-63
(3)
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pp. 620-656
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Keyword(s):
1992 ◽
Vol 114
(2)
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pp. 571-571
1982 ◽
Vol 52
(1)
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pp. 109-147
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2020 ◽
Vol 0
(1 (1355))
◽
pp. 23-33
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2016 ◽
Vol 368
(11)
◽
pp. 8267-8294
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1998 ◽
Vol 57
(3)
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pp. 706-720
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