Mathematics · Functional Analysis
Which of the following statements is true for an arbitrary normed linear space U?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1The closed unit ball in U is compact.
- 2For every x ∈ U, we have ||x|| = sup||f||≤1 |f(x)|, where f denotes elements of the dual space U.
- 3U is isomorphic to its double-dual U.
- 4Every bounded linear functional from U to &mathbb;R is continuous.✓
Correct answer
Every bounded linear functional from U to &mathbb;R is continuous.
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