# Tagged Questions

0answers
62 views

### Open map in Banach algebra

I'm having trouble showing a certian function is open and can be extended. Let $\Omega$ be a completely regular topological space and $A=C_b(\Omega)$ the space of all complex-values bounded ...
2answers
94 views

### Banach-algebra homeomorphism.

Let $A$ be a commutative unital Banach algebra that is generated by a set $Y \subseteq A$. I want to show that $\Phi(A)$ is homeomorphic to a closed subset of the Cartesian product \$ ...
1answer
118 views

### Is the space of bounded functions with the Supremum norm a Banach Algebra

X is an arbitrary , non empty set, B(X) the set of bounded functions $f:X\rightarrow \mathbb{R}$ and $||f||_\infty = \sup_{x\in X }|f(x)|$. Is $(B(X),||.||_\infty )$ a Banach Algebra? My attempt ...
0answers
43 views

### Prove that if $A$ is algebra generated by $\sin(x)$ and $\cos(x)$ then $A = \{ f\in C_b(\mathbb R ) : f(t) = f(t + 2\pi )$ for all $t \in \mathbb R\}$ [duplicate]

Possible Duplicate: Finding a closed subalgebra generated by functions. Let $A$ be the uniformly closed subalgebra of $C_b(\mathbb{R} )$ generated by $\sin(x)$ and $\cos(x)$. Prove: \$A = ...
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