The Index of Invariant Subspaces of Bounded below Operators on Banach Spaces

• 作者: George Chailos
• 来源期刊: 理论数学进展(英文)
• 学科: 数学
• 关键词: INDEX INVARIANT SUBSPACES BOUNDED below OPERATORS BANACH Spaces
• 年，卷（期）: 2012,（2）
• 页码范围: 124-127
• 页数: 4页
• 分类号: O1

摘要

For an operator on a Banach space , let be the collection of all its invariant subspaces. We consider the index function on and we show, amongst others, that if is a bounded below operator and if , , then If in addition are index 1 invariant subspaces of , with nonzero intersection, we show that . Furthermore, using the index function, we provide an example where for some , holds .