Linear functional analysis
著者
書誌事項
Linear functional analysis
（Springer undergraduate mathematics series）
Springer, c2000
- : pbk
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注記
Includes bibliographical references (p. 267) and index
内容説明・目次
内容説明
This introduction to the ideas and methods of linear functional analysis shows how familiar and useful concepts from finite-dimensional linear algebra can be extended or generalized to infinite-dimensional spaces. Aimed at advanced undergraduates in mathematics and physics, the book assumes a standard background of linear algebra, real analysis (including the theory of metric spaces), and Lebesgue integration, although an introductory chapter summarizes the requisite material. The highlights of the second edition include: a new chapter on the Hahn-Banach theorem and its applications to the theory of duality. This chapter also introduces the basic properties of projection operators on Banach spaces, and weak convergence of sequences in Banach spaces - topics that have applications to both linear and nonlinear functional analysis; extended coverage of the uniform boundedness theorem; and plenty of exercises, with solutions provided at the back of the book.
目次
Preliminaries.- Normed Spaces.- Inner Product Spaces, Hilbert Spaces.- Linear Operators.- Duality and the Hahn-Banach Theorem.- Linear Operators on Hilbert Spaces.- Compact Operators.- Integral and Differential Equations.- Solutions to Exercises.- Further Reading.- References.- Notation Index.- Index.
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