Joint Spectral Radius, Operator Semigroups, and a Problem of W. Wojtyński

✍ Scribed by Victor S. Shulman; Yuriı V. Turovskiı

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 361 KB
• Volume: 177
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.2000.3640

✦ Synopsis

We investigate the connections between the invariant subspace problem for operator semigroups and the joint spectral radius. As a consequence, it is proved that any quasinilpotent Lie algebra of compact operators on a Banach space is triangularizable. We extend the Berger Wang formula to precompact sets of essentially scalar operators and prove the continuity of the joint spectral radius on them.