Locally convex spaces [electronic resource] / M. Scott Osborne.
2014
QA322
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Details
Title
Locally convex spaces [electronic resource] / M. Scott Osborne.
Author
Osborne, M. Scott, author.
ISBN
9783319020457 electronic book
3319020455 electronic book
9783319020440
3319020447
3319020455 electronic book
9783319020440
3319020447
Published
Cham : Springer, 2014.
Language
English
Description
1 online resource (viii, 213 pages) : illustrations.
Item Number
10.1007/978-3-319-02045-7 doi
Call Number
QA322
Dewey Decimal Classification
515.7
Summary
For most practicing analysts who use functional analysis, the restriction to Banach spaces seen in most real analysis graduate texts is not enough for their research. This graduate text, while focusing on locally convex topological vector spaces, is intended to cover most of the general theory needed for application to other areas of analysis. Normed vector spaces, Banach spaces, and Hilbert spaces are all examples of classes of locally convex spaces, which is why this is an important topic in functional analysis. While this graduate text focuses on what is needed for applications, it also shows the beauty of the subject and motivates the reader with exercises of varying difficulty. Key topics covered include point set topology, topological vector spaces, the Hahn-Banach theorem, seminorms and Frechet spaces, uniform boundedness, and dual spaces. The prerequisite for this text is the Banach space theory typically taught in a beginning graduate real analysis course.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Description based on online resource; title from PDF title page (SpringerLink, viewed November 11, 2013).
Series
Graduate texts in mathematics ; 269. 0072-5285
Available in Other Form
Original 9783319020440
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Table of Contents
Topological Groups
Topological Vector Spaces
Locally Convex Spaces
The Classics
Dual Spaces
Duals of Frechet Spaces
A Topological Oddities
B Closed Graphs in Topological Groups
C The Other Krein?Smulian Theorem
D Further Hints for Selected Exercises.
Topological Vector Spaces
Locally Convex Spaces
The Classics
Dual Spaces
Duals of Frechet Spaces
A Topological Oddities
B Closed Graphs in Topological Groups
C The Other Krein?Smulian Theorem
D Further Hints for Selected Exercises.