Let $A$ be a Banach algebra. Is there a Banach algebra $B$ which unitaly contains $A$ but the spectrum of each elements of $B$ has empty interior(as a subset of $\mathbb{C}$)?

The motivatiob comes from the fact that the spectrum of elements in a smaller algebra possibly loses its interior when we compute its spectrum in a larger algebra.(Rudin, Functional analysis(

Let $A$ be a Banach algebra. Is there a Banach algebra $B$ which contains $A$ but the spectrum of each elements of $B$ has empty interior(as a subset of $\mathbb{C}$)?

The motivation comes from the fact that the spectrum of elements in a smaller algebra possibly loses its interior when we compute its spectrum in a larger algebra.(Rudin, Functional analysis)