Category:Unitizations of Normed Algebras

This category contains results about Unitizations of Normed Algebras.
Definitions specific to this category can be found in Definitions/Unitizations of Normed Algebras.

Let $\GF \in \set {\R, \C}$.

Let $\struct {A, \norm {\, \cdot \,} }$ be a normed algebra over $\GF$ that is not unital as an algebra.

Let $A_+$ be the unitization of $A$.

Define $\norm {\, \cdot \,}_{A_+} : A_+ \to \hointr 0 \infty$ by:

$\norm {\tuple {x, \lambda} }_{A_+} = \norm x + \cmod \lambda$

for each $\tuple {x, \lambda} \in A_+$.

We call $\struct {A_+, \norm {\, \cdot \,}_{A_+} }$ the unitization of $\struct {A, \norm {\, \cdot \,} }$.