Bounded Operator - Properties of The Space of Bounded Linear Operators

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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