Definition:Normed Algebra

Definition

Let $R$ be a division ring with norm $\norm {\,\cdot\,}_R$.

A normed algebra over $R$ is a pair $\struct {A, \norm{\,\cdot\,} }$ where:

$A$ is a algebra over $R$

$ \norm{\,\cdot\,} $ is an algebra norm on $A$.

Also see

• Definition:Algebra over Ring
• Definition:Norm on Algebra
• Definition:Normed Unital Algebra
• Definition:Normed Vector Space

• Results about normed algebras can be found here.

Sources

• 2017: Amol Sasane: A Friendly Approach to Functional Analysis ... (previous) ... (next): Chapter $\S 2.4$: Composition of continuous linear transformations