User:Caliburn/s/fa/Definition:Space of Bounded Linear Transformations/Inner Product Space
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Definition
Let $\struct {V, \innerprod \cdot \cdot_V}$ and $\struct {U, \innerprod \cdot \cdot_U}$ be inner product spaces.
Then the space of bounded linear transformations from $V$ to $U$, $\map B {V, U}$, is defined by:
- $\map B {V, U} = \set {A : V \to U \mid A \text { is a bounded linear transformation} }$