Millionaire Mode

Banach Spaces

Question 1 of 15

Let $X$ be a Banach space and $T: X \rightarrow X$ be a linear operator. Which of the following statements is true?

  1. If $T$ is bounded, then it is continuous.
  2. If $T$ is continuous, then it is bounded.
  3. If $T$ is compact, then it is bounded.
  4. If $T$ is bounded, then it is compact.

Prize Money

15₹7 Crores
14₹1 Crore
13₹50,00,000
12₹25,00,000
11₹12,50,000
10₹6,40,000
9₹3,20,000
8₹1,60,000
7₹80,000
6₹40,000
5₹20,000
4₹10,000
3₹5,000
2₹2,000
1₹1,000