Brouwer's Fixed Point Theorem (Proof)

Given a Banach space (L,\|\cdot\|), its dual space is L^{\prime... | Filo

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.,