05364nam 2200733Ia 450 991081947600332120200520144314.01-281-92814-39786611928148981-277-542-0(CKB)1000000000549270(EBL)1223509(SSID)ssj0000307499(PQKBManifestationID)11238226(PQKBTitleCode)TC0000307499(PQKBWorkID)10244194(PQKB)10961968(MiAaPQ)EBC1223509(WSP)005319v12(Au-PeEL)EBL1223509(CaPaEBR)ebr10255380(CaONFJC)MIL192814(OCoLC)854974045(EXLCZ)99100000000054927020040505d2003 uy 0engur|n|---|||||txtccrQuantum probability communications /Stephane Attal, J.Martin Lindsay1st ed.Singapore ;London World Scientific20031 online resource (294 p.)QP-PQ ;12Description based upon print version of record.981-238-974-1 Includes bibliographical references.CONTENTS; 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(Γ).; 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.CONCLUSIONBIBLIOGRAPHICAL 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 SPACES4. 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 TIMES15. 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 ALGEBRAS1. 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.2.2.2. Definition of von Neumann algebras.Lecture 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.QP-PQ ;12.ProbabilitiesQuantum theoryStochastic processesMarkov processesProbabilities.Quantum theory.Stochastic processes.Markov processes.530.12Lindsay J. Martin1611471Attal S(Stephane)0MiAaPQMiAaPQMiAaPQBOOK9910819476003321Quantum probability communications3939750UNINA