TY  - BOOK
AU  - Osborne,M.Scott
TI  - Locally Convex Spaces
T2  - Graduate Texts in Mathematics,
SN  - 9783319020457
U1  - 515.7 23
PY  - 2014///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Functional analysis
KW  - Lie groups
KW  - Topological groups
KW  - Functional Analysis
KW  - Topological Groups, Lie Groups
N1  - 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
N2  - 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
ER  -