Locally Convex Spaces / by M. Scott Osborne.

Format:

Book

Author/Creator:

Osborne, M. Scott, Author.

Series:

Graduate Texts in Mathematics, 0072-5285 ; 269

Language:

English

Subjects (All):

Functional analysis.

Topological groups.

Lie groups.

Functional Analysis.

Topological Groups, Lie Groups.

Local Subjects:

Functional Analysis.

Topological Groups, Lie Groups.

Physical Description:

1 online resource (VIII, 213 p. 5 illus.)

Edition:

1st ed. 2014.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2014.

Language Note:

English

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 Fréchet 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.

Contents:

1 Topological Groups

2 Topological Vector Spaces

3 Locally Convex Spaces

4 The Classics

5 Dual Spaces

6 Duals of Fré chet Spaces

A Topological Oddities

B Closed Graphs in Topological Groups

C The Other Krein–Smulian Theorem

D Further Hints for Selected Exercises

Bibliography

Index.

Notes:

Bibliographic Level Mode of Issuance: Monograph

ISBN:

3-319-02045-5