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Jajte R. — Strong Limit Theorems in Noncommutative L2-Spaces
Jajte R. — Strong Limit Theorems in Noncommutative L2-Spaces

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Название: Strong Limit Theorems in Noncommutative L2-Spaces

Автор: Jajte R.

Аннотация:

The noncommutative versions of fundamental classical results on the almost sure convergence in L2-spaces are discussed: individual ergodic theorems, strong laws of large numbers, theorems on convergence of orthogonal series, of martingales of powers of contractions etc. The proofs introduce new techniques in von Neumann algebras. The reader is assumed to master the fundamentals of functional analysis and probability. The book is written mainly for mathematicians and physicists familiar with probability theory and interested in applications of operator algebras to quantum statistical mechanics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2008

Количество страниц: 113

Добавлена в каталог: 04.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Algebra of von Neumann      1
Almost orthogonal operators      41
Conditional expectation      4 23 53 85 88
Conditional expectation of Accardi — Cecchini      91
Contraction, generated by a kernel      4 10 17 52
Contraction, normal      38
Contraction, positive definite      52
Convergence of conditional expectations      86
Convergence of martingales      34 86
Convergence, almost sure      2
Convergence, almost uniform      2
Convergence, strong      2
Convergence, uniform      3
Dual map      4
Dynamical semigroup      22 23
Endomorphism      4 31 32
Ergodic Hilbert transform      47 49
Filtration      86 88
Invariant state      13
Invariant vector      20
Kernel      4 10 17
Local ergodic theorem      10 22 28
Map, $\phi$-contractive      4
Map, positive      4
Map, Schwarz      4
Martingale      88
Maximal ergodic theorem      11 14 58
Mean ergodic theorem      18 46 57 91
Modular automorphism      19
Modular conjugation      91
Modular operator      19
Operator, modular      19
Operator, normal      38
Operator, unitary      37 46 47 49
Orthogonal projection      53 86 88
Orthogonal sequence      64 68 74 78
orthogonal series      64
Positive cone      91 92
Positive contraction      91
Positive map      4
Random Ergodic Theorem      31
Schwarz map      4
Semigroup of contractions      22 23
Semigroup of Schwarz maps      21
Semigroup, quantum dynamical      22 23
Semigroup, weak * conditions      25
Sequence of iterates      52
Sequence, orthogonal      64 68 74 75 78
Sequence, quasi-orthogonal      69 77 84
Sequence, weakly stationary      62
Shift transformation      33
Spectral measure      37 53
Spectral representation      38 46 53
Spectrum      37
Strong Law of Large Numbers      64 78
Tensor product, algebra      31
Tensor product, state      31
Theorem of Akcoglu      91
Theorem of Burkholder and Chow      53
Theorem of Goldstein      11 86
Theorem of Rademacher — Menshov      64 68 69
Theorem of Stein      52 92
Theorem of von Neumann      53
Transformation, preserving measure      31
Transformation, ultraweakly measurable      32
Transformation, weakly measurable      32
Vector, cyclic      1
Vector, separating      1
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