On the Coarse Geometry of James Spaces
2019 ◽
Vol 63
(1)
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pp. 77-93
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AbstractIn this note we prove that the Kalton interlaced graphs do not equi-coarsely embed into the James space ${\mathcal{J}}$ nor into its dual ${\mathcal{J}}^{\ast }$. It is a particular case of a more general result on the non-equi-coarse embeddability of the Kalton graphs into quasi-reflexive spaces with a special asymptotic structure. This allows us to exhibit a coarse invariant for Banach spaces, namely the non-equi-coarse embeddability of this family of graphs, which is very close to but different from the celebrated property ${\mathcal{Q}}$ of Kalton. We conclude with a remark on the coarse geometry of the James tree space ${\mathcal{J}}{\mathcal{T}}$ and of its predual.
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1965 ◽
Vol 17
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pp. 367-372
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2000 ◽
Vol 13
(2)
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pp. 137-146
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2008 ◽
Vol 33
(1)
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pp. 111
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2001 ◽
Vol 43
(1)
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pp. 125-128
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2012 ◽
Vol 365
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pp. 1051-1079
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2005 ◽
Vol 2005
(3)
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pp. 221-227
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