All Questions

Problem. Is the separability of the Gelfand space of a semi-simple commutative Banach algebra $A$ equivalent to the existence of a countable family $\{\varphi_n\}_{n\in\omega}$ of multiplicative ...

I'm trying to determine whether or not the standard proof that the spectrum of a point in a unital Banach algebra is non-empty can be adapted to prove the same thing over certain non-Archimedean ...

Here is a little theorem that I'm trying to prove. I haven't seen it in literature before, but I think the applications will be quite useful, particularly in the context of Banach algebras. Denote ...

Let $K$ be a compact subset of $\Bbb C$. Let $\mathcal P(K)$ be the closed algebra generated by the complex polynomials on $K$. What is the character space $\Phi_{\mathcal P(K)}$ of $\mathcal P(K)$?...

I have been reading the paper Determining elements in $C^∗$-algebras through spectral properties. The paper discusses about what would be the relation be between two elements $a$ and $b$ of a Banach ...