LEADER 06598nam 2200529 450 001 996483154103316 005 20230717142412.0 010 $a9783031072468$b(electronic bk.) 010 $z9783031072451 035 $a(MiAaPQ)EBC7052705 035 $a(Au-PeEL)EBL7052705 035 $a(CKB)24285899400041 035 $a(OCoLC)1337946447 035 $a(PPN)263902897 035 $a(EXLCZ)9924285899400041 100 $a20230107d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAnalysis and quantum groups /$fLars Tuset 210 1$aCham, Switzerland :$cSpringer Nature Switzerland AG,$d[2022] 210 4$d©2022 215 $a1 online resource (632 pages) 311 08$aPrint version: Tuset, Lars Analysis and Quantum Groups Cham : Springer International Publishing AG,c2022 9783031072451 320 $aIncludes bibliographical references and index. 327 $aIntro -- Preface -- Contents -- 1 Introduction -- 2 Banach Spaces -- 2.1 Normed Spaces -- 2.2 Operators on Banach Spaces -- 2.3 Linear Functionals -- 2.4 Weak Topologies -- 2.5 Extreme Points -- 2.6 Fixed Point Theorems -- 2.7 The Eberlein-Krein-Smulian Theorems -- 2.8 Reflexivity and Functionals Attaining Extreme Values -- 2.9 Compact Operators on Banach Spaces -- 2.10 Complemented and Invariant Subspaces -- 2.11 An Approximation Property -- 2.12 Weakly Compact Operators -- Exercises -- 3 Bases in Banach Spaces -- 3.1 Schauder Bases -- 3.2 Unconditional Convergence -- 3.3 Equivalent Bases -- 3.4 Dual Bases -- 3.5 The James Space J -- Exercises -- 4 Operators on Hilbert Spaces -- 4.1 Hilbert Spaces -- 4.2 Fourier Transform Over the Reals -- 4.3 Fourier Series -- 4.4 Polar Decomposition of Operators on Hilbert Spaces -- 4.5 Compact Normal Operators -- 4.6 Fredholm Operators -- 4.7 Traceclass and Hilbert-Schmidt Operators -- Exercises -- 5 Spectral Theory -- 5.1 Spectral Theory for Banach Algebras -- 5.2 Spectral Theory for C*-Algebras -- 5.3 Ideals and Hereditary Subalgebras -- 5.4 The Borel Spectral Theorem -- 5.5 Von Neumann Algebras -- 5.6 The ?-Weak Topology -- 5.7 The Kaplansky Density Theorem -- 5.8 Maximal Commutative Subalgebras -- 5.9 Unit Balls and Extremal Points in C*-Algebras -- Exercises -- 6 States and Representations -- 6.1 States -- 6.2 The GNS-Representation -- 6.3 Pure States -- 6.4 Primitive Ideals and Prime Ideals -- 6.5 Postliminal C*-Algebras -- 6.6 Direct Limits -- Exercises -- 7 Types of von Neumann Algebras -- 7.1 The Lattice of Projections -- 7.2 Normalcy -- 7.3 Center Valued Traces -- 7.4 Semifinite von Neumann Algebras -- 7.5 Classification of Factors -- Exercises -- 8 Tensor Products -- 8.1 Tensor Products of C*-Algebras -- 8.2 Von Neumann Tensor Products -- 8.3 Completely Positive Maps -- 8.4 Hilbert Modules. 327 $aExercises -- 9 Unbounded Operators -- 9.1 Definitions and Basic Properties -- 9.2 The Cayley Transform -- 9.3 Sprectral Theory for Unbounded Operators -- 9.4 Generalized Convergence of Unbounded Operators -- Exercises -- 10 Tomita-Takesaki Theory -- 10.1 Left and Right Hilbert Algebras -- 10.2 Weight Theory -- 10.3 Weights and Left Hilbert Algebras -- 10.4 Weights on C*-Algebras -- 10.5 The Modular Automorphism -- 10.6 Centralizers of Weights -- 10.7 Cocycle Derivatives -- 10.8 A Generalized Radon-Nikodym Theorem -- 10.9 Standard Form -- 10.10 Spatial Derivative -- 10.11 Weights and Conditional Expectations -- 10.12 The Extended Positive Part of a von Neumann Algebra -- 10.13 Operator Valued Weights -- Exercises -- 11 Spectra and Type III Factors -- 11.1 The Arveson Spectrum -- 11.2 The Connes Spectrum -- 11.3 Classification of Type III Factors -- Exercises -- 12 Quantum Groups and Duality -- 12.1 Hopf Algebras -- 12.2 Compact Quantum Groups -- 12.3 Locally Compact Quantum Groups -- 12.4 A Fundamental Involution -- 12.5 Density Conditions -- 12.6 The Coinverse -- 12.7 Relative Invariance -- 12.8 Invariance and the Modular Element -- 12.9 Modularity and Manageability -- 12.10 The Dual Quantum Group -- Exercises -- 13 Special Cases -- 13.1 The Universal Quantum Group -- 13.2 Commutative and Cocommutative Quantum Groups -- 13.3 Amenability -- Exercises -- 14 Classical Crossed Products -- 14.1 Crossed Products of Actions -- 14.2 Takesaki-Takai Duality -- 14.3 Landstad Theory -- 14.4 Examples of Crossed Products -- Exercises -- 15 Crossed Products for Quantum Groups -- 15.1 Complete Left Invariance for Locally Compact Quantum Groups -- 15.2 Coactions and Integrability -- 15.3 Crossed Products of Coactions -- 15.4 Corepresentation Implementation of Coactions -- Exercises -- 16 Generalized and Continuous Crossed Products -- 16.1 Cocycle Crossed Products. 327 $a16.2 Cocycle Bicrossed Products -- 16.3 Continuous Coactions and Regularity -- Exercises -- 17 Basic Construction and Quantum Groups -- 17.1 Basic Construction for Crossed Products of Quantum Groups -- 17.2 From the Basic Construction to Quantum Groups -- Exercises -- 18 Galois Objects and Cocycle Deformations -- 18.1 Galois Objects -- 18.2 Deformation of C*-Algebras by Continuous Unitary 2-Cocycles -- Exercises -- 19 Doublecrossed Products of Quantum Groups -- 19.1 Radon-Nikodym Derivatives of Weights Under Coactions -- 19.2 Doublecrossed Products -- 19.3 Morphisms of Quantum Groups and Associated Right Coactions -- 19.4 More on Doublecrossed Products -- Exercises -- 20 Induction -- 20.1 Inducing Corepresentations Using Modular Theory -- Exercises -- Appendix -- A.1 Set Theoretic Preliminaries -- A.2 Cardinality and Bases of Vector Spaces -- A.3 Topology -- A.4 Nets and Induced Topologies -- A.5 The Stone-Weierstrass Theorem -- A.6 Measurability and Lp-Spaces -- A.7 Radon Measures -- A.8 Complex Measures -- A.9 Product Integrals -- A.10 The Haar-Measure -- A.11 Holomorphic Functional Calculus -- A.12 Applications to Linear Algebra and Differential Equations -- A.13 The Theorems of Carleson, Runge and Phragmen-Lindelöf -- Exercises -- Bibliography -- Index. 606 $aFunctional analysis 606 $aGroup theory 606 $aHarmonic analysis 606 $aGrups quàntics$2thub 608 $aLlibres electrònics$2thub 615 0$aFunctional analysis. 615 0$aGroup theory. 615 0$aHarmonic analysis. 615 7$aGrups quàntics 676 $a515.7 700 $aTuset$b Lars$01252224 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a996483154103316 996 $aAnalysis and Quantum Groups$92902902 997 $aUNISA LEADER 01809nam 2200325 450 001 9910412326003321 005 20230825164237.0 035 $a(CKB)5280000000243715 035 $a(NjHacI)995280000000243715 035 $a(EXLCZ)995280000000243715 100 $a20230825d2020 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIWOCL '20 $eproceedings of the International Workshop on OpenCL /$fAssociation for Computing Machinery 210 1$aNew York, New York :$cAssociation for Computing Machinery,$d2020. 215 $a1 online resource (104 pages) $cillustrations 311 $a1-4503-7531-6 330 $aThe International Workshop for OpenCL (IWOCL, which is pronounced "eye-wok-ul") was conceived in a meeting between Simon McIntosh-Smith and Ben Bergen at the Los Alamos National Laboratory on May 8th, 2012. McIntosh-Smith and Bergen lamented that there were no organized workshops or meetings for the rapidly growing OpenCL community. After testing this idea with colleagues over the next few months, they decided to create the kind of OpenCL conference they wanted to go to themselves, and thus IWOCL was born. Since then, the trend to develop heterogeneous and parallel programs in C++ has grown strongly, a trend addressed by the SYCL standard, which, like OpenCL, is also from the Khronos group. This year IWOCL has evolved into IWOCL / SYCLcon, to embrace the growing importance of SYCL in the wider community. 606 $aOpenCL (Computer program language) 615 0$aOpenCL (Computer program language) 676 $a005.275 801 0$bNjHacI 801 1$bNjHacl 906 $aBOOK 912 $a9910412326003321 996 $aIWOCL '20$93473669 997 $aUNINA