Study On The Operators And The Spectrum Of The Operators On Banach Space

Master thesis "Study on the Operators and the Spectrum of the Operators on Banach Space" is the organic combinative result of the study on the theory of Ba-nach space and the operator theory of functional analysis. There are four chapters in the paper. Chapterl mainly introduces some basic results about the generalized symmetric idempotent operator and the fine structure of spectrum under certain conditions. In chapter 2, the property of essentially contained were studied in more in-depth discussion. On this basis, we construct three new operators. Moreover, we discuss their nature and the structure of spectrum. Then we get some beautiful conclusions. In chapter 3, we study the equivalent characterization of the comple-mented singular operator which is under certain conditions and the relationship with the reflexive Banach spaces. Further more, we generalize the second chapter-related content. In chapter 4, We mainly discuss the other operator classes and give two property of elementary operator.In addition, a feature of this article is that we construct some new operators and research their properties.