Definition:Normed Unital Algebra
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Definition
Let $R$ be a division ring with norm $\norm {\,\cdot\,}_R$.
A normed unital algebra over $R$ is a pair $\struct {A, \norm {\,\cdot\,} }$ where:
- $A$ is a unital algebra over $R$
- $\norm {\,\cdot\,}$ is a norm on $A$.
Also see
- Definition:Unital Algebra over Ring
- Definition:Norm on Unital Algebra
- Definition:Normed Algebra
- Definition:Normed Vector Space
- Results about normed unital algebras can be found here.
Sources
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