# Category:Banach Algebras

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This category contains results about **Banach Algebras**.

Definitions specific to this category can be found in Definitions/Banach Algebras.

Let $R$ be either the real numbers $\R$ or the complex numbers $\C$..

Let $\struct {A, \circ}$ be an algebra over $R$ which is also a Banach space.

Then $\struct {A, \circ}$ is a **Banach algebra** if and only if:

- $\forall a, b \in R: \norm {a \circ b} \le \norm a \norm b$

where $\norm {\, \cdot \,}$ denotes the norm on $A$.

## Subcategories

This category has the following 3 subcategories, out of 3 total.

## Pages in category "Banach Algebras"

The following 8 pages are in this category, out of 8 total.