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: $ 0.02万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=574090
• 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巴纳赫空间和正算子的理论。正性是泛函分析的一个重要领域，在不同的科学学科中有许多应用，包括数理经济学，这是我的次要研究领域。该理论最有趣的开放问题之一是不变子空间问题（ISP）： Banach 格子上的任何正算子 T 是否具有非平凡的闭合不变子空间？ 在拟议的研究中，我们希望采用一种不同的新方法来解决这个问题，即使用集值映射的不动点定理。这种方法似乎能够在不假设 T 是准幂的情况下工作，因此预计将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有序巴拿赫空间中的问题。徒劳地，我想研究后一类有序 Banach 空间中正算子的 ISP。此外，独立于 ISP，我想通过考虑实心锥体来进一步扩展反射锥体的研究，并将这些类型的锥体与 Radon Nikodym 属性联系起来。