Topological Uniform Descent And Single-valued Extension Property

Spectral theory has been a hot issue of operator theory, especially in recen-t decades, with the rapid development of technology, operator spectral theory’s application is more and more deeply in quantum information theory, quantum me-chanics, physics and other cross-disciplines. While single-valued extension property and topological uniform descent property are regarded as an important branch of the theory, therefore their research will also become especially important.This text is primarily based on the spectral theory of bounded linear operator, research and give the relationship between its topological uniform descent property and single-valued extension property.Also using the relationship discuss its stability, and on this basis, we also using a-Weyl theory to explore the relationship between topological uniform descent property and a-Browder theory.This paper is divided into three chapters:The first chapter gives a research background, definition and property of various spectrum, as well as both of the definition of topological uniform descent property and the single-valued extension property.The second chapter using the spectral theory gives a series of equivalent con-ditions to predicate single-valued extension property, and discuss the stability of the single-valued extension property.The third chapter according to the a-Weyl theory,explore the relationship be-tween topological uniform descent property and a-Browder theory.