LEADER 03316nam 22006135 450 001 9910300150503321 005 20200703223354.0 010 $a3-319-02045-5 024 7 $a10.1007/978-3-319-02045-7 035 $a(CKB)3710000000078589 035 $a(SSID)ssj0001067641 035 $a(PQKBManifestationID)11592632 035 $a(PQKBTitleCode)TC0001067641 035 $a(PQKBWorkID)11092440 035 $a(PQKB)11066086 035 $a(DE-He213)978-3-319-02045-7 035 $a(MiAaPQ)EBC3107032 035 $a(PPN)176105298 035 $a(EXLCZ)993710000000078589 100 $a20131106d2014 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aLocally Convex Spaces /$fby M. Scott Osborne 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (VIII, 213 p. 5 illus.) 225 1 $aGraduate Texts in Mathematics,$x0072-5285 ;$v269 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-02044-7 327 $a1 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. 330 $aFor most practicing analysts who use functional analysis, the restriction to Banach spaces seen in most real analysis graduate texts is not enough for their research. This graduate text, while focusing on locally convex topological vector spaces, is intended to cover most of the general theory needed for application to other areas of analysis.  Normed vector spaces, Banach spaces, and Hilbert spaces are all examples of classes of locally convex spaces, which is why this is an important topic in functional analysis. While this graduate text focuses on what is needed for applications, it also shows the beauty of the subject and motivates the reader with exercises of varying difficulty. Key topics covered include point set topology, topological vector spaces, the Hahn?Banach theorem, seminorms and Fréchet spaces, uniform boundedness, and dual spaces. The prerequisite for this text is the Banach space theory typically taught in a beginning graduate real analysis course. 410 0$aGraduate Texts in Mathematics,$x0072-5285 ;$v269 606 $aFunctional analysis 606 $aTopological groups 606 $aLie groups 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132 615 0$aFunctional analysis. 615 0$aTopological groups. 615 0$aLie groups. 615 14$aFunctional Analysis. 615 24$aTopological Groups, Lie Groups. 676 $a515.73 700 $aOsborne$b M. Scott$4aut$4http://id.loc.gov/vocabulary/relators/aut$062669 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300150503321 996 $aLocally convex spaces$9257832 997 $aUNINA