Page "Banach space" Paragraph 2

If X and Y are Banach spaces over the same ground field K, the set of all continuous K-linear maps T: X → Y is denoted by B ( X, Y ).

In infinite-dimensional spaces, not all linear maps are automatically continuous.

In general, a linear mapping on a normed space is continuous if and only if it is bounded on the closed unit ball.

Thus, the vector space B ( X, Y ) can be given the operator norm