000 05601nam a22005175i 4500
001 978-3-662-21558-6
003 DE-He213
005 20190213151457.0
007 cr nn 008mamaa
008 130625s1993 gw | s |||| 0|eng d
020 _a9783662215586
_9978-3-662-21558-6
024 7 _a10.1007/978-3-662-21558-6
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
_2thema
072 7 _aPBWL
_2thema
082 0 4 _a519.2
_223
100 1 _aMeyer, Paul-André.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aQuantum Probability for Probabilists
_h[electronic resource] /
_cby Paul-André Meyer.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1993.
300 _aX, 293 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1538
505 0 _aI: Non Commutative Probability -- II: Spin -- III: The Harmonic Oscillator -- IV: Fock Space (1) -- V. Multiple Fock Spaces -- VI. Stochastic Calculus on Fock Space -- VII. Independence -- Appendix 1: Functional Analysis -- Hilbert-Schmidt operators (1) -- Trace class operators (2) -- Duality properties (3) Weak convergence properties (4) -- Weak topologies for operators (5) -- Tensor products of Hilbert spaces (6–7) -- Appendix 2: Conditioning and Kernels -- Conditioning: discrete case (1) -- Conditioning: continuous case (2) -- Example of the canonical pair (3) -- Multiplicity theory (4) -- Classical kernels (5) -- Non commutative kernels, first form (6) -- second form (7) -- Completely positive maps (8) -- Some difficulties (9) -- Appendix 3: Two Events -- 1. Elementary theory -- Application of spectral theory (2) -- Some elementary properties (3) -- Positive elements (4) -- Symbolic calculus for s.a. elements (5) -- Applications (6) -- Characterization of positive elements (7) -- A few inequalities (8) -- Existence of many states (1) -- Representations and the GNS theorem (2–3) -- Examples from toy Fock space theory (4) -- Quotient algebras and approximate units (5) -- 3. Von Neumann algebras -- Weak topologies and normal states (1) -- Von Neumann’s bicommutant theorem (2–3) -- Kaplanski’s density theorem (4) -- The predual (5) -- Normality and order continuity (6) -- About integration theory (7) -- Measures with bounded density (8) -- The linear Radon-Nikodym theorem (9) -- The KMS condition (10) -- Entire vectors (11) -- 4. The Tomita-Takesaki theory -- Elementary geometric properties (1) -- The main operators (2–3) -- Interpretation of the adjoint (4) -- The modular property (5) -- Using the linear RN theorem (6) -- The main computation (7) -- The three main theorems (8) -- Additional results (9) -- Examples (10) -- Appendix 5: Local Times and Fock Space -- 1. Dynkin’s formula -- Symmetric Markov semigroups and processes (1) -- Dynkin’s formula (2) -- Sketch of the Marcus-Rosen approach to the continuity of local times (3) -- 2. Le Jan’s “supersymmetric” approach -- Notations of complex Brownian motion (1) -- Computing the Wiener product (2) -- Stratonovich integral and trace (4) -- Expectation of the exponential of an element of the second chaos (5) -- Exponential formula in the antisymmetric case (7) -- Supersymmetric Fock space: the Wick and Wiener products (8) -- Properties of the Wiener product (9) -- Applications to local times (sketch) (10) -- References -- Index of Notation.
520 _aThese notes contain all the material accumulated over six years in Strasbourg to teach "Quantum Probability" to myself and to an audience of commutative probabilists. The text, a first version of which appeared in successive volumes of the Seminaire de Probabilite8, has been augmented and carefully rewritten, and translated into international English. Still, it remains true "Lecture Notes" material, and I have resisted suggestions to publish it as a monograph. Being a non-specialist, it is important for me to keep the moderate right to error one has in lectures. The origin of the text also explains the addition "for probabilists" in the title : though much of the material is accessible to the general public, I did not care to redefine Brownian motion or the Ito integral. More precisely than "Quantum Probability" , the main topic is "Quantum Stochastic Calculus" , a field which has recently got official recognition as 81825 in the Math.
650 0 _aDistribution (Probability theory.
650 1 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
650 2 4 _aTheoretical, Mathematical and Computational Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19005
650 2 4 _aOptics, Lasers, Photonics, Optical Devices.
_0http://scigraph.springernature.com/things/product-market-codes/P31030
650 2 4 _aQuantum Optics.
_0http://scigraph.springernature.com/things/product-market-codes/P24050
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540564768
776 0 8 _iPrinted edition:
_z9783662215593
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1538
856 4 0 _uhttps://doi.org/10.1007/978-3-662-21558-6
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c10810
_d10810