On the spectrum of derivatives and automorphisms of Banach algebras. (Spanish) Zbl 0606.46032
The authors discuss necessary and sufficient conditions for a compact set K in the complex plane to be the spectrum of a derivation or of an automorphism in a Banach algebra with nontrivial multiplication, as follows.
1) K is the spectrum of a derivation if and only if there exist points p, q in K such that \(p+q\in K.\)
2) If \(0\not\in K\), then k is the spectrum of an automorphism if and only if there exist points p,q\(\in K\) such that pq\(\in K\).
1) K is the spectrum of a derivation if and only if there exist points p, q in K such that \(p+q\in K.\)
2) If \(0\not\in K\), then k is the spectrum of an automorphism if and only if there exist points p,q\(\in K\) such that pq\(\in K\).
Reviewer: R.M.Range
MSC:
| 46H05 | General theory of topological algebras |
| 47B47 | Commutators, derivations, elementary operators, etc. |
