Tagged Questions
4
votes
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 ...
4
votes
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 $ ...
0
votes
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 ...
1
vote
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 = ...
