4
votes
2answers
47 views

Minkowski type inequality in Banach algebras

Under which circumstances it is true that $\|(A+B)^n\|^{1/n}\le \|A^n\|^{1/n}+\|B^n\|^{1/n}$ for elements $A$ and $B$ in a Banach algebra and a natural number $n$?
3
votes
1answer
87 views

What is the generator of the disc algebra

The disc algebra, as a set, consists of the functions on the unit disc $D$, which are analytic on the interior of the disc and continuous on its boundary. Its addition and multiplication is obvious. ...
3
votes
1answer
126 views

Do non-commutative algebras with dense commutative subalgebras exist?

Let $A$ be a normed unital algebra. Suppose that $C\subseteq A$ is a commutative subalgebra which is dense in $A$. I ask myself the following question: Under the above assumptions, is $A$ necessarily ...