巴拿赫空间理论引论

《巴拿赫空间来自理论引论》是2003年世界图书出版公司出版的图书，作者是R.E.Megginson。

• 作者 R.E.Megginson
• 出版社 世界图书出版公司
• 出版时间 2003年6月
• 页数 596 页
• 定价 58 元

内容介绍

　　Since the study of normed s来自paces for their 360百科own sake evol顶经马波行ved rather than arose fully formed, there is some room to disagree about who founded the field. Albert Bennett came close to giving the definition of a normed space in 导处犯犯课被政处娘a 1916 paper [23] on an extension of Newton's method for finding root外却村九效殖到升影获几s, and in 1918 Frederic Rie稳空宗庆帮七声系字针安sz [195] based a general种击求张冷按晚ization of the Fredholm theory of integral equations on the defin运市足比及此倍据械损财ing axioms of a complete 优的温主娘丝兵够青苦最normed space, though he did not use these axioms to study the general theory of such spac映检际增逐倍适直互海es. According to Jean Dieudonne [64], Riesz had at this time conside二推无沉企陈元王red devel上oping a general theory of complete normed spaces, but never published anything in this direction业湖资细业往强穿虽. In a paper that appeared in 1921, Eduard Helly [102] proved what is now 味called Helly's theorem fo型队审乱放困把酒案升r bounded linear functionals. Along the way, he developed some of the general theory of normed spaces, but only in the context of norms on subspaces of the ve片特ctor space of all sequences of complex scalars.

　　本书为英文版。

作品目录

　　Prefa阻叶星穿怀阶或晚两交星ce

　　1 Basic Concepts

　　1.1 Preliminaries

　　1.2 Norms

　　1.3 First Properties of Normed Spaces

　　1.4 Linear Operators Be倒爱功药教益深础tween Normed Spaces

　　1.5 Bak叶审培岩缩今顺e Category

　　1片研酒须止促仅九时.6 Three Fundamental Theorems

　　1.7 Quotient Spaces

　　1.8 Direct Sums

　　1.9 The Hahn-Banach Extension Theorems

　　1.10 Dual Spaces

　　1.11 The Second Dual and Reflexivity

　　1.12 Separability

　　1.13 Characterizations of Reflexivity

　　2 The Weak and Weak Topologies

　　2.1 Topology and Nets

　　2.2 Vector Topologies

　　2.3 Metrizable Vector Topologies

　　2.4 Topologies Induced by Families of Functions

　　2.5 The Weak Topology

　　2.6 The Weak Topology

　　2.7 The Bounded Weak Topology

　　2.8 Weak Compactness

　　2.9 Jamess Weak Compacteness Theorem

　　2.10 Support Points and Subreflexivity

　　2.11 Support Points and Subreflexivity

　　3 Linear Operators

　　3.1 Adjoint Operators

　　3.2 Projections and Complemented Subspaces

　　3.3 Banach Algebras and Spectra

　　3.4 Compact Operators

　　3.5 Weakly Compact Operators

　　4 Schauder Bases

　　4.1 First Properties of Schauder Bases

　　4.2 Unconditional Bases

　　4.3 Equivalent Bases

　　4.4 Bases and Duality

　　4.5 Jamess Space J

　　5 Rotundity and Smoothness

　　5.1 Rotundity

　　5.2 Uniform Rotundity

　　5.3 Generalztions of Uniform Rotundity

　　5.4 Smoothness

　　5.5 Unifrom Smoothness

　　5.6 Generaliztions of Unifrom Smoothness

　　A Prerequistes

　　B Metric Spaces

　　C The Spaces lp and en/p， 1≤p≤∞

　　D Ultranets

　　References

　　List of Symbols

　　Index