Category:Unital Banach Algebras

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This category contains results about Unital Banach Algebras.

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

Let $\struct {A, \norm \cdot}$ be a Banach algebra over $\Bbb F$ that is unital as an algebra and:

$A \ne \set { {\mathbf 0}_A}$

Let ${\mathbf 1}_A$ be the identity element of $A$.

We say that $A$ is a unital Banach algebra if and only if:

$\norm {\mathbf 1_A} = 1$

Subcategories

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

B

Boundary of Spectrum of Element in Subalgebra of Unital Banach Algebra‎ (3 P)

E

Element of Unital Banach Algebra on Boundary of Group of Units of Subalgebra is Not Invertible in Algebra‎ (2 P)

S

Spectrum of Element of Unital Commutative Banach Algebra‎ (3 P)

Pages in category "Unital Banach Algebras"

The following 14 pages are in this category, out of 14 total.

B

C

E

G

Group of Units in Unital Banach Algebra is Open

I

Inverse Mapping on Group of Units in Unital Banach Algebra is Continuous

M

Maximal Ideal of Unital Commutative Banach Algebra is Kernel of Character

N

Norm of Inverse of Sequence of Invertible Elements Converging to Non-Invertible Element in Unital Banach Algebra

R

Resolvent Set of Element in Banach Algebra has same Unique Unbounded Component as Resolvent Set of Element in Closed Subalgebra

S

U

Unital C*-Algebra is Unital Banach Algebra

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Banach Algebras