Real Banach algebras as \(\mathcal C(\mathcal K)\) algebras (Q2907032)

The paper deals with representations of Banach algebras. For example, it is shown that a Banach algebra \(A\) is \(C(K)\)-representable if and only if its spectral radius \(r\) satisfies the condition \(r(a^2)\leq r(a^2+b^2)\) for all \(a, b\in A\). It is also shown that a commutative real Banach algebra is \(C(K)\)-representable if and only if \(A\) is strictly real. Some other ways of representing a commutative real Banach algebra are considered as well.