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Linear Functional Analysis. Bryan P. Rynne , Martin A. 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 initial chapters develop the theory of infinite-dimensional normed spaces, in particular Hilbert spaces, after which the emphasis shifts to studying operators between such spaces.

Functional analysis has applications to a vast range of areas of mathematics; the final chapters discuss the particularly important areas of integral and differential equations. Further 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; plenty of exercises, with solutions provided at the back of the book.

Inner Product Spaces Hilbert Spaces. Compact Operators. Integral and Differential Equations. Linear Operators. Linear Operators on Hilbert Spaces. Solutions to Exercises. Notation Index. Linear Functional Analysis Bryan P. Normed Spaces. Further Reading.

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## Linear Functional Analysis

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 initial chapters develop the theory of infinite-dimensional normed spaces, in particular Hilbert spaces, after which the emphasis shifts to studying operators between such spaces. Functional analysis has applications to a vast range of areas of mathematics; the final chapters discuss the particularly important areas of integral and differential equations. 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;. A particularly useful feature is the material on compact operators and applications to differential equations. Skip to main content Skip to table of contents.

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## Linear Functional Analysis - Springer Undergraduate Mathematics Series

Linear Functional Analysis. Bryan Rynne , M. This book provides an introduction to the ideas and methods of linear fu- tional analysis at a level appropriate to the? The prerequisites for reading it are a standard undergraduate knowledge of linear algebra and real analysis including the t- ory of metric spaces. Part of the development of functional analysis can be traced to attempts to?

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It seems that you're in Germany. We have a dedicated site for Germany. Authors: Rynne , Bryan, Youngson , M. 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.

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Linear Functional Analysis. Bryan P. Rynne , Martin A. 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 initial chapters develop the theory of infinite-dimensional normed spaces, in particular Hilbert spaces, after which the emphasis shifts to studying operators between such spaces. Functional analysis has applications to a vast range of areas of mathematics; the final chapters discuss the particularly important areas of integral and differential equations.