LEADER 03382nam 2200601 a 450 001 9910438151503321 005 20200520144314.0 010 $a3-642-34369-4 024 7 $a10.1007/978-3-642-34369-8 035 $a(CKB)2670000000533485 035 $a(EBL)1156710 035 $a(OCoLC)831115742 035 $a(SSID)ssj0000854864 035 $a(PQKBManifestationID)11453784 035 $a(PQKBTitleCode)TC0000854864 035 $a(PQKBWorkID)10912705 035 $a(PQKB)10527832 035 $a(DE-He213)978-3-642-34369-8 035 $a(MiAaPQ)EBC1156710 035 $a(PPN)168326752 035 $a(EXLCZ)992670000000533485 100 $a20130105d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aPositive linear maps of operator algebras /$fErling Strmer 205 $a1st ed. 2013. 210 $aHeidelberg [Germany] ;$aNew York $cSpringer$d2013 215 $a1 online resource (134 p.) 225 0$aSpringer monographs in mathematics,$x1439-7382 300 $aDescription based upon print version of record. 311 $a3-642-34368-6 311 $a3-642-42913-0 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- 1 Generalities for positive maps -- 2 Jordan algebras and projection maps -- 3 Extremal positive maps -- 4 Choi matrices and dual functionals -- 5 Mapping cones -- 6 Dual cones -- 7 States and positive maps -- 8 Norms of positive maps -- Appendix: A.1 Topologies on B(H) -- A.2 Tensor products -- A.3 An extension theorem -- Bibliography -- Index . 330 $aThis volume, setting out the theory of positive maps as it stands today, reflects the rapid growth in this area of mathematics since it was recognized in the 1990s that these applications of C*-algebras are crucial to the study of entanglement in quantum theory. The author, a leading authority on the subject, sets out numerous results previously unpublished in book form. In addition to outlining the properties and structures of positive linear maps of operator algebras into the bounded operators on a Hilbert space, he guides readers through proofs of the Stinespring theorem and its applications to inequalities for positive maps.  The text examines the maps? positivity properties, as well as their associated linear functionals together with their density operators. It features special sections on extremal positive maps and Choi matrices. In sum, this is a vital publication that covers a full spectrum of matters relating to positive linear maps, of which a large proportion is relevant and applicable to today?s quantum information theory. The latter sections of the book present the material in finite dimensions, while the text as a whole appeals to a wider and more general readership by keeping the mathematics as elementary as possible throughout.  . 410 0$aSpringer Monographs in Mathematics,$x1439-7382 606 $aOperator algebras 606 $aC*-algebras 615 0$aOperator algebras. 615 0$aC*-algebras. 676 $a512.9/4 676 $a512.94 700 $aStrmer$b Erling$0598654 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438151503321 996 $aPositive Linear Maps of Operator Algebras$92507403 997 $aUNINA