Properties of The Space of Bounded Linear Operators
- The space of all bounded linear operators from U to V is denoted by B(U,V) and is a normed vector space.
- If V is Banach, then so is B(U,V),
- from which it follows that dual spaces are Banach.
- For any A in B(U,V), the kernel of A is a closed linear subspace of U.
- If B(U,V) is Banach and U is nontrivial, then V is Banach.
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