Linear Maps Preserving the Spectral Radius

✍ Scribed by Matej Brešar; Peter Šemrl

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 402 KB
• Volume: 142
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1996.0153

✦ Synopsis

Let X be a complex Banach space. If 8: B(X) Ä B(X) is a surjective linear map such that A and 8(A) have the same spectral radius for every A # B(X), then 8=c3 where 3 is either an algebra-automorphism or an antiautomorphism of B(X) and c is a complex constant such that |c|=1.