Invariant subspaces of positive operators

正算子的不变子空间

• 批准号: 435513-2013
• 负责人: Xanthos, Foivos
• 金额: $ 0.94万
• 依托单位: Ryerson University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=669022
• 关键词: Invariant; subspaces; positive; operators

My primary area of research is the theory of Ordered Banach spaces and positive operators. Positivity is an important field of Functional analysis that has many applications in different disciplines of sciences, including mathematical economics, which is my secondary area of research. One of the most interesting open problems of this theory, is the Invariant Subspace Problem(ISP):****Does any positive operator T on a Banach lattice have a non trivial closed invariant subspace?****In the proposed research we want to adopt a different and new approach to this problem, which is the use of fixed point theorems of set-valued maps. This approach seems that is able to work without the assumption that T is quasinilpotent, hence it is expected tol bring new insight to this problem. ****So far, in my research I have been studying problems in Ordered Banach spaces that lack lattice structure. In this vain, I want to study the ISP for positive operators in the latter class of Ordered Banach spaces. Moreover independently with the ISP, I want to further extend the study of reflexive cones by considering solid cones and relate these type of cones with the Radon Nikodym Property.******

我的主要研究领域是有序的Banach空间和积极运营商的理论。积极性是功能分析的重要领域，在包括数学经济学在内的不同学科中具有许多应用，这是我的次要研究领域。该理论中最有趣的开放问题之一是不变的子空间问题（ISP）：****在Banach晶格上的任何积极的操作员是否都有非琐碎的封闭不变的子空间？这种方法似乎可以在没有假设是quasinilpotent的情况下起作用，因此可以预期为这个问题带来新的见解。 ****到目前为止，在我的研究中，我一直在研究缺乏晶格结构的Banach空间的问题。在这一徒劳的情况下，我想研究后者有序的Banach空间中积极运营商的ISP。此外，与ISP独立，我想通过考虑固体锥并将这些类型的锥与ra耐尼科迪的特性联系起来进一步扩展反射锥的研究。******