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Catalogue Information
Field name	Details
Dewey Class	515.73
Title	Locally Convex Spaces ([EBook]) / by M. Scott Osborne.
Author	Osborne, M. Scott
Other name(s)	SpringerLink (Online service)
Publication	Cham Springer International Publishing 2014.
Physical Details	VIII, 213 pages:. 5 illus. : online resource.
ISBN	9783319020457
Summary Note	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 note	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.
System details note	Online access to this digital book is restricted to subscription institutions and access is available through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-319-02045-7
Links to Related Works	Subject References: Functional Analysis . Locally convex spaces . Mathematics . Topological groups . Topological groups, Lie groups . Authors: Osborne, M. Scott . Corporate Authors: SpringerLink (Online service) . Series: Graduate texts in mathematics . GTM . Classification: 515.73 . 515.73 (DDC 23) .

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Locally Convex Spaces

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