Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Analysis Normed Linear Spaces
Let X, Y and Z be Banach spaces. Suppose that T : X → Y is linear and S : Y → Z is linear, bounded and injective. In addition, if S ◦ T : X → Z is bounded, then, which of the following statements is TRUE?
1
T is surjective
2
T is bounded but not continuous
3
T is bounded
4
T is not bounded