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anonymous
  • Member for 14 years
  • Last seen more than 7 years ago
  • Berlin, Germany
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Geometric implications of $\beta(B_X) = 2$
We're only interested in infinite-dimensional spaces here.
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Geometric implications of $\beta(B_X) = 2$
@Dirk It is shown in the article by Elton and Odell which Bill Johnson has just mentioned (available e.g. from eudml.org/doc/266720) that $\beta(B_X)$ is always strictly greater than 1.
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Geometric implications of $\beta(B_X) = 2$
@Dirk I'm not actually sure if such spaces exist. I've now added examples that show $\beta(B_X) = 2$ also for $\ell^1$ and $L^1[0,1]$. Maybe $\sqrt 2$ is actually the minimal value for $\beta(B_X)$.
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Geometric implications of $\beta(B_X) = 2$
Complete distinction of cases
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What are the major differences between real and complex Banach space?
While the general Bishop–Phelps theorem is false for complex Banach spaces, it is worth noting that it holds for complex Banach space X with the Radon–Nikodym property.
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What are the major differences between real and complex Banach space?
The answer is of course "yes" on 1-dimensional real Hilbert spaces.
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Characterization of Schur's property
I agree that this is the easier direction the Eberlein–Šmulian theorem.
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Trace theorem for $C^{k,1}$ domains
Paste in the abstract and link (in preparation for the deletion of my own, superfluous answer -- hope this is not too bold!)
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