LEADER 03267nam 22005175 450 001 9910484305503321 005 20251113211856.0 010 $a3-030-47465-8 024 7 $a10.1007/978-3-030-47465-2 035 $a(CKB)4100000011665191 035 $a(DE-He213)978-3-030-47465-2 035 $a(MiAaPQ)EBC6455971 035 $a(PPN)252514920 035 $a(EXLCZ)994100000011665191 100 $a20201215d2021 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 13$aAn Introduction to C*-Algebras and the Classification Program /$fby Karen R. Strung ; edited by Francesc Perera 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2021. 215 $a1 online resource (XIII, 322 p.) 225 1 $aAdvanced Courses in Mathematics - CRM Barcelona,$x2297-0312 311 08$a3-030-47464-X 327 $aBanach algebras and spectral theory -- The Gelfand representation -- C*-algebra basics -- Positive elements -- Positive linear functionals and representations -- Weak and strong operator topologies and von Neumann algebras -- Tensor products for C*-algebras -- Completely positive maps -- Inductive limits and approximately finite (AF) C*-algebras -- Group C*-algebras and crossed products -- Cuntz algebras -- Quasidiagonal C*-algebras -- K-theory for unital C*-algebras -- Classification of AF-algebras -- Nuclear dimension -- Strongly self-absorbing algebras -- The Jiang-Su algebra -- Strict comparison and the Cuntz semigroup -- The Classification Theorem and the Toms-Winter Theorem. 330 $aThis book is directed towards graduate students that wish to start from the basic theory of C*-algebras and advance to an overview of some of the most spectacular results concerning the structure of nuclear C*-algebras. The text is divided into three parts. First, elementary notions, classical theorems and constructions are developed. Then, essential examples in the theory, such as crossed products and the class of quasidiagonal C*-algebras, are examined, and finally, the Elliott invariant, the Cuntz semigroup, and the Jiang-Su algebra are defined. It is shown how these objects have played a fundamental role in understanding the fine structure of nuclear C*-algebras. To help understanding the theory, plenty of examples, treated in detail, are included. This volume will also be valuable to researchers in the area as a reference guide. It contains an extensive reference list to guide readers that wish to travel further. 410 0$aAdvanced Courses in Mathematics - CRM Barcelona,$x2297-0312 606 $aFunctional analysis 606 $aAlgebra 606 $aFunctional Analysis 606 $aOrder, Lattices, Ordered Algebraic Structures 615 0$aFunctional analysis. 615 0$aAlgebra. 615 14$aFunctional Analysis. 615 24$aOrder, Lattices, Ordered Algebraic Structures. 676 $a512.55 700 $aStrung$b Karen R.$01220965 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484305503321 996 $a-Algebras and the Classification Program$94463149 997 $aUNINA