All Questions

Let $H$ be an infinite-dimensional Hilbert space and let $\mathcal{B}(H)$ be the (C*/W*-)algebra of bounded operators on it. Actually, you may forget about the involution in $\mathcal{B}(H)$ because I ...

Is there a real-world example of a Banach *-algebra with a nonzero *-radical (intersection of kernels of all *-representations)? Textbooks give examples of finite-dimensional algebras with degenerate ...

For a given unital Banach *-algebra $A$, let us put $A_+=\{\sum_1^n x^*_ix_i : x_i\in A, n\in \mathbb{N}\}$. We write $x\geq0$ if $x\in A_+$. What types of (non semi-simple) unital Banach *-algebras ...

Let $A$ be a commutative unital Banach algebra.The maximal ideal space of $A$ is denoted by $\hat A$. Assume that $D:A \to A$ is a derivation. Fix an element $a\in A$. Assume that for every $\phi\in \...

Let $\mathcal{A}$ be a non-reflexive Banach algebra. For the definition of Arens product, please refer to this link. Here we let $\square$ denote the first Arens product and $\diamond$ denote the ...

What is an example of two Banach algebras $A$ and $B$, and an algebra map $\phi:A \to B$ which is not continuous?