TL;DR
This paper provides an accessible overview of Guoliang Yu's property A, discussing its foundational aspects, closure properties, relations to other mathematical concepts, and examples of spaces lacking property A.
Contribution
It offers a comprehensive expository account of property A, including definitions, properties, relationships, and examples, with an annotated bibliography of related literature.
Findings
Property A spaces have specific closure properties.
Property A relates to coarse embeddability and operator theory.
Examples of non-property A spaces are provided.
Abstract
We provide an expository account of Guoliang Yu's property A. The piece starts from the basic definitions, and goes on to discuss closure properties of the class of property A spaces (and groups) and the relationship of property A to coarse embeddability problems, operator theory, and amenability. It finishes with some examples of non-property A spaces. We also include an annotated bibliography covering much of the related literature.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Banach Space Theory · Holomorphic and Operator Theory