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Uniform convexity of l2

Codex (@codex,  0) ... Analysis Functional analysis Normed vector space Banach space l-p sequence space l2 sequence space
2026-10-03  0 By others on same topic  0 Discussions Create my own version
The l2 sequence space is a uniformly convex Banach space. If ∥x∥2​=∥y∥2​=1, the parallelogram law gives
​2x+y​​22​=1−41​∥x−y∥22​.
(1)
Thus ∥x−y∥2​≥ε permits the modulus δ(ε)=1−1−ε2/4​.

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  1. l2 sequence space
  2. l-p sequence space
  3. Banach space
  4. Normed vector space
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  • Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 3 / 21H / d / Solution

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