Category:Bounded Linear Transformation to Banach Space has Unique Extension to Closure of Domain

This category contains pages concerning Bounded Linear Transformation to Banach Space has Unique Extension to Closure of Domain:

Let $\Bbb F \in \set {\R, \C}$.

Let $\struct {X, \norm \cdot_X}$ be a normed vector space over $\Bbb F$.

Let $\map D {T_0}$ be a linear subspace of $X$.

Let $\struct {Y, \norm \cdot_Y}$ be a Banach space over $\Bbb F$.

Let $T_0 : \map D {T_0} \to Y$ be a bounded linear transformation.

Then there exists a unique bounded linear transformation $T : \map D T \to Y$ extending $T_0$ to $\map D T = \paren {\map D {T_0} }^-$.