Search Results

Suppose that $X$ be a compact space and $\left|\cdot\right|$ be an algebra norm on $C(X)$ Is every algebra norm $\left|\cdot\right|$ on $C(X)$ equivalent to uniform norm $\left|\cdot\right|_ …

I've asked this question here Let $A$ be a Banach algebra with identity $e_A$, I'd like to find $\operatorname{Rad}(A/\operatorname{Rad}(A)).$ whre we define $\operatorname{Rad}(A)=\{a\i …

I have the following two questions 1: Let $A$ and $B$ be Banach algebras and suppose that $B$ is semisimple. Let $T:A \to B $ be a homomorphism with $\overline {TA}=B.$ Is $T$ automatically continu …

Let $A$ and $B$ be commutative Banach algebra. I have proven that if $A$ and $B$ have identity $e_A$ and $e_B$ respectivly , then $e_A\hat\otimes e_B$ is identity for $A\hat\otimes B$ (the projectiv …

Let $X$ be a compact subset of $\mathbb {C^n}$. The polynomial convex hall of $X$ is the set $\hat{X}=\{z\in \mathbb {C^n}: \left|P(z) \right|\leq \left||P |\right|_\infty , \text{for all polynomial …

Let $\mathcal{A}$ be a commutative weakly amenable Banach algebra and $\mathcal{B}$ be a Banach algebra, let $\theta:\mathcal{A} \to \mathcal{B}$ be a continuous homomorphism with dense range; then it …

I am looking for examples of amenable Banach algebras which have non-amenable subalgebra I know 1: Each amenable Banach algebra has a bounded approximate identity 2: If $I$ be a closed ideal in a …

A Banach algebra $A$ is contractible if $H^1(A, X)=0$ for all Banach $A$-bimodules $X$. Now to my question Let $A$ be Banach algebra and $I$ be closed ideal of $A$. If $I$ and $A/I$ are both cont …