M. Scott Osborne: Locally Convex Spaces

Cover: 9783319020440 | Locally Convex Spaces | M. Scott Osborne | Buch | viii | Englisch

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

M. Scott Osborne is currently Professor Emeritus of Mathematics at the University of Washington.

Zusammenfassung

Introduces functional analysis while focusing on locally convex spaces

Focuses on applications to other topics in analysis

Contains over 100 exercises with varying levels of difficulty to motivate the reader

Inhaltsverzeichnis

¿¿¿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.

Details

Erscheinungsjahr:	2013
Fachbereich:	Analysis
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	viii 213 S. 5 s/w Illustr. 213 p. 5 illus.
ISBN-13:	9783319020440
ISBN-10:	3319020447
Sprache:	Englisch
Einband:	Gebunden
Autor:	Osborne, M. Scott
Hersteller:	Springer International Publishing
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 18 mm
Von/Mit:	M. Scott Osborne
Erscheinungsdatum:	22.11.2013
Gewicht:	0,506 kg