Find an example of two Banach spaces whose Banach-Mazur distanc... | Filo
Find an example of two Banach spaces whose Banach-Mazur dist…
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SOLVED:Show that if a Banach space X admits a strictly convex (rotund) norm and also a norm with the Kadec-Klee property, then X admits an LUR norm. Note that there are spaces that admit Kadec-Klee norms and no norm that is LUR (Haydon; see, e.g., [DGZ3]). The space ℓ∞ admits a strictly convex norm but no LUR norm (Lindenstrauss, Troyanski; see, e.g.,
SOLVED:Show that if a Banach space X admits a strictly convex (r…
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