Structural properties of Banach spaces and of bounded operators acting on them

Banach 空间和作用于其上的有界算子的结构性质

• 批准号: 341767-2013
• 负责人: Tcaciuc, Adi
• 金额: $ 0.8万
• 依托单位: Grant MacEwan University
• 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=572361
• 关键词: Structural; properties; Banach; spaces; bounded

This proposal is in Functional Analysis and is mainly devoted to the investigation of structural properties of infinite dimensional Banach spaces and of bounded operators acting on them. The first project continues a very successful investigation initiated in the previous grant proposal and deals with a new notion of invariance for bounded linear operators. We call this new notion "almost invariance" and examine under which condition bounded operators have non-trivial almost invariant subspaces. The second project deals with the construction of Banach spaces without approximation property. We are examining conditions to obtain these constructions inside Banach spaces from certain large classes of spaces. The third project deals with the construction of a Banach space with very unexpected properties: it has non-trivial type, yet it contains no copy of well known classical spaces or of a reflexive space.

这个建议是在功能分析，主要致力于调查的结构特性， 无穷维Banach空间和作用于其上的有界算子。 第一个项目延续了前一个拨款提案中非常成功的调查，并涉及有界线性算子的不变性的新概念。我们称之为“几乎不变性”的新概念，并研究在何种条件下有界算子有非平凡的几乎不变子空间。 第二个项目涉及不具有逼近性质的Banach空间的构造。我们 检查条件，以获得这些建设内Banach空间从某些大型类的空间。 第三个项目涉及一个Banach空间的建设非常意想不到的性质：它有 非平凡类型，但它不包含众所周知的经典空间或自反空间的副本。