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: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635267
• 关键词: Structural; properties; Banach; spaces; bounded

This proposal is in Functional Analysis and is mainly devoted to the investigation of structural properties ofinfinite 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 areexamining 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 hasnon-trivial type, yet it contains no copy of well known classical spaces or of a reflexive space.

这篇论文发表在泛函分析中，主要研究有限维巴拿赫空间的结构性质和作用于其上的有界算子。第一个项目延续了之前拨款提案中非常成功的研究，并处理了有界线性算子的不变性的新概念。我们称这个新概念为“几乎不变性”，并检验在什么条件下有界算子具有非平凡几乎不变性子空间。第二个项目涉及无近似性质的Banach空间的构造。我们正在研究从某些大的空间类中获得这些巴拿赫空间内结构的条件。第三个项目涉及Banach空间的构造，它具有非常意想不到的属性：它具有非平凡类型，但它不包含众所周知的经典空间或自反空间的副本。