Joint Spectral Radius, Operator Semigroups, and a Problem of W. Wojtyński☆
Joint Spectral Radius, Operator Semigroups, and a Problem of W. Wojtyński☆
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DOI：
10.1006/jfan.2000.3640
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发表时间：
2000-11
影响因子：
1.7
通讯作者：
V. Shulman;Yuriĭ V. Turovskiĭ
中科院分区：
文献类型：
--
作者：
V. Shulman;Yuriĭ V. Turovskiĭ
摘要研究了算子半群的不变子空间问题与联合谱半径之间的关系。由此证明了Banach空间上任何紧算子的拟幂零李代数都是可三角化的。我们将Berger-Wang公式推广到本质纯量算子的预紧集上，并证明了它们的联合谱半径的连续性。
Abstract 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.