LEADER 05364nam 2200733Ia 450 001 9910819476003321 005 20200520144314.0 010 $a1-281-92814-3 010 $a9786611928148 010 $a981-277-542-0 035 $a(CKB)1000000000549270 035 $a(EBL)1223509 035 $a(SSID)ssj0000307499 035 $a(PQKBManifestationID)11238226 035 $a(PQKBTitleCode)TC0000307499 035 $a(PQKBWorkID)10244194 035 $a(PQKB)10961968 035 $a(MiAaPQ)EBC1223509 035 $a(WSP)005319v12 035 $a(Au-PeEL)EBL1223509 035 $a(CaPaEBR)ebr10255380 035 $a(CaONFJC)MIL192814 035 $a(OCoLC)854974045 035 $a(EXLCZ)991000000000549270 100 $a20040505d2003 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aQuantum probability communications /$fStephane Attal, J.Martin Lindsay 205 $a1st ed. 210 $aSingapore ;$aLondon $cWorld Scientific$d2003 215 $a1 online resource (294 p.) 225 1 $aQP-PQ ;$v12 300 $aDescription based upon print version of record. 311 $a981-238-974-1 320 $aIncludes bibliographical references. 327 $aCONTENTS; CONTENTS OF QPC XI; PREFACE for QPC Volumes XI & XII; INTEGRAL-SUM KERNEL OPERATORS; 0. INTRODUCTION; 1. FINITE POWER SETS; 1.1. Some products on F(?).; 1.2. Product functions.; 1.3. Guichardet Space.; 2. INTEGRAL-SUM CONVOLUTIONS; 2.1. Duality Transforms.; 2.2. Formal Derivation.; 2.3. Basic Estimate.; 3. QUANTUM WIENER INTEGRALS; 4. INTEGRAL-SUM KERNEL OPERATORS; 4.1. Basic Estimate.; 4.2. Uniqueness of the kernel.; 4.3. Reconstruction of kernel from operator.; 4.4. Algebras of integral-sum kernel operators.; 4.5. Four argument integral-sum kernels.; 4.6. Matrix-valued kernels. 327 $aCONCLUSIONBIBLIOGRAPHICAL NOTES; REFERENCES; QUANTUM PROBABILITY APPLIED TO THE DAMPED HARMONIC OSCILLATOR; 1. THE FRAMEWORK OF QUANTUM PROBABILITY; 2. SOME QUANTUM MECHANICS; 3. CONDITIONAL EXPECTATIONS AND OPERATIONS; 4. SECOND QUANTISATION; 5. UNITARY DILATIONS OF SPIRALING MOTION; 6. THE DAMPED HARMONIC OSCILLATOR; REFERENCES; QUANTUM PROBABILITY AND STRONG QUANTUM MARKOV PROCESSES; 0. INTRODUCTION; I. Quantum Probability; 1. A COMPARATIVE DESCRIPTION OF CLASSICAL AND QUANTUM PROBABILITY; 2. THE ROLE OF TENSOR PRODUCTS OF HILBERT SPACES; 3. SOME BASIC OPERATORS ON FOCK SPACES 327 $a4. FROM URN MODEL TO CANONICAL COMMUTATION RELATIONSII. Quantum Markov Processes; 5. STOCHASTIC OPERATORS ON C*-ALGEBRAS; 6. STINESPRING'S THEOREM; 7. EXTREME POINTS OF THE CONVEX SET OF STOCHASTIC OPERATORS; 8. STINESPRING'S THEOREM IN TWO STEPS; 9. CONSTRUCTION OF A QUANTUM MARKOV PROCESS; 10. THE CENTRAL PART OF MINIMAL DILATION; 11. ONE PARAMETER SEMIGROUPS OF STOCHASTIC MAPS ON A C*-ALGEBRA; III. Strong Markov Processes; 12. NONCOMMUTATIVE STOP TIMES; 13. MARKOV PROCESS AT SIMPLE STOP TIMES; 14. MINIMAL MARKOV FLOW AT SIMPLE STOP TIMES 327 $a15. STRONG MARKOV PROPERTY OF THE MINIMAL FLOW FOR A GENERAL STOP TIME16. STRONG MARKOV PROPERTY UNDER A SMOOTHNESS CONDITION; 17. A QUANTUM VERSION OF DYNKIN'S LOCALIZATION FORMULA; ACKNOWLEDGEMENTS; REFERENCES; LIMIT PROBLEMS FOR QUANTUM DYNAMICAL SEMIGROUPS - INSPIRED BY SCATTERING THEORY; 0. INTRODUCTION; 1. COMPARISON OF THE LARGE TIME BEHAVIOUR OF TWO SEMIGROUPS; 2. THE CLASSIFICATION OF STATES; 3. ERGODIC PROPERTIES OF QUANTUM DYNAMICAL SEMIGROUPS; 4. CONVERGENCE TOWARDS THE EQUILIBRIUM; ACKNOWLEDGEMENT; REFERENCES; A SURVEY OF OPERATOR ALGEBRAS; 0. COMPLEX BANACH ALGEBRAS 327 $a1. C*-ALGEBRAS1.1. Definition and first spectral properties.; 1.2. Adding a unit.; 1.3. First examples: abelian C*-aIgebras.; 1.4. Continuous functional calculus in C*-algebras.; 1.5. More examples: B(H) and its sub-C*-algebras.; 1.6. Order Structure, states, and t h e GNS construction.; 1.6.1. Positive elements and order in A.; 1.6.2. Dual order structure and states.; 1.6.3. GNS construction.; 2. VON NEUMANN ALGEBRAS; 2.1. Some topologies on B(H).; 2.1.1. Three natural topologies.; 2.1.2. The ideal L1(H); 2.2. von Neuman algebras.; 2.2.1. von Neumann bicommutant theorem. 327 $a2.2.2. Definition of von Neumann algebras. 330 $aLecture notes from a Summer School on Quantum Probability held at the University of Grenoble are collected in these two volumes of the QP-PQ series. The articles have been refereed and extensively revised for publication. It is hoped that both current and future students of quantum probability will be engaged, informed and inspired by the contents of these two volumes. An extensive bibliography containing the references from all the lectures is included in Volume 12. 410 0$aQP-PQ ;$v12. 606 $aProbabilities 606 $aQuantum theory 606 $aStochastic processes 606 $aMarkov processes 615 0$aProbabilities. 615 0$aQuantum theory. 615 0$aStochastic processes. 615 0$aMarkov processes. 676 $a530.12 701 $aLindsay$b J. Martin$01611471 701 $aAttal$b S$g(Stephane)$00 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910819476003321 996 $aQuantum probability communications$93939750 997 $aUNINA