User:Caliburn/s/fa/Definition:Space of Bounded Linear Transformations/Normed Vector Space

Definition

Let $\struct {V, \norm \cdot_V}$ and $\struct {U, \norm \cdot_U}$ be normed vector spaces.

Then the space of bounded linear transformations from $V$ to $U$, $\map B {V, U}$, is defined by:

$\map B {V, U} = \set {A : V \to U \mid A \text { is a bounded linear transformation} }$