Mathematics · Functional Analysis
Consider X = {u | u: [0, 1] → &mathbb;R is continuous and u(0) = 0} with the supremum norm ||u|| = supx ∈ [0, 1]|u(x)|. Let T(u) = ∫01 u(t) dt and S = {|T(u)| : u ∈ X, ||u|| ≤ 1}. Which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
Share:
- 1S is a closed subset of &mathbb;R.
- 2There exists u ∈ X such that ||u|| = 1 and T(u) = 1.
- 3S is a bounded subset of &mathbb;R and sup(S) = 1.✓
- 4S is an unbounded subset of &mathbb;R.
Correct answer
S is a bounded subset of &mathbb;R and sup(S) = 1.
Download Single Question PDF
Save this question and verified answer as a clean study sheet with live clickable link.
👥
Share with Friends & Study Groups
Challenge your peer aspirants on WhatsApp or Telegram to solve this question!
Online Test Series
Start Free Mock Test →Preparing for Mathematics?
Practice full-length mock tests with real exam timers, instant score analysis, and all-India ranking.
Chapter Practice
Practice Functional Analysis MCQs →Want more practice questions on Functional Analysis?
Solve complete topic-wise tests with detailed solutions on GkGet.
Related Practice Questions
Recommended practice questions in Mathematics · Functional Analysis