An individual ergodic theorem for positive linear mapping of von Neumann algebras

1981 ◽  
Vol 14 (4) ◽  
pp. 303-304 ◽  
Author(s):  
M. Sh. Gol'dshtein
Keyword(s):  
Ergodic Theorem ◽  
Von Neumann Algebras ◽  
Linear Mapping ◽  
Von Neumann ◽  
Individual Ergodic Theorem

Ergodic theorems for semifinite von Neumann algebras: II

1980 ◽  
Vol 88 (1) ◽  
pp. 135-147 ◽  
Author(s):  
F. J. Yeadon
Keyword(s):  
Banach Spaces ◽  
Ergodic Theorem ◽  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
Operator Norm ◽  
Ergodic Theorems ◽  
Unbounded Operators ◽  
Von Neumann ◽  
The Mean ◽  
Image Position

In (7) we proved maximal and pointwise ergodic theorems for transformations a of a von Neumann algebra which are linear positive and norm-reducing for both the operator norm ‖ ‖∞ and the integral norm ‖ ‖1 associated with a normal trace ρ on . Here we introduce a class of Banach spaces of unbounded operators, including the Lp spaces defined in (6), in which the transformations α reduce the norm, and in which the mean ergodic theorem holds; that is the averagesconverge in norm.

scholarly journals On individual subsequential ergodic theorem in von Neumann algebras

2001 ◽  
Vol 145 (1) ◽  
pp. 55-62 ◽  
Author(s):  
Semyon Litvinov ◽  
Farrukh Mukhamedov
Keyword(s):  
Ergodic Theorem ◽  
Von Neumann Algebras ◽  
Von Neumann

Martingale convergence in von Neumann algebras

1978 ◽  
Vol 84 (1) ◽  
pp. 47-56 ◽  
Author(s):  
E. Christopher Lance
Keyword(s):  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
Positive Element ◽  
Linear Mapping ◽  
Von Neumann ◽  
Positive Mapping ◽  
Image Position ◽  
Martingale Convergence

Let N be a von Neumann subalgebra of a von Neumann algebra M. A linear mapping π: M → N is called a retraction if it is idempotent and has norm one. By a result of Tomiyama(15) a retraction is a positive mapping and is a module homo-morphism over N. A retraction is normal if it is ultraweakly continuous, and faithful if it does not annihilate any nonzero positive element of M. Suppose that (Nn)n≥1 is an increasing sequence of von Neumann subalgebras of M whose union is weakly dense in M and that, for each n, πn: M → Nn is a faithful normal retraction. The sequence (πn) is called a martingale if, whenever m ≥ n,

Lectures on von Neumann Algebras

2019 ◽  
Author(s):  
Serban-Valentin Stratila ◽  
Laszlo Zsido
Keyword(s):  
Von Neumann Algebras ◽  
Von Neumann

Probability Theory for Fuzzy Quantum Spaces with Statistical Applications

2017 ◽  
Author(s):  
Renáta Bartková ◽  
Beloslav Riečan ◽  
Anna Tirpáková
Keyword(s):  
Probability Theory ◽  
Fuzzy Sets ◽  
Ergodic Theorem ◽  
Intuitionistic Fuzzy Sets ◽  
Mathematics Students ◽  
Intuitionistic Fuzzy ◽  
Individual Ergodic Theorem ◽  
Recurrence Theorem ◽  
The Individual ◽  
Atanassov Intuitionistic Fuzzy Sets

The reference considers probability theory in two main domains: fuzzy set theory, and quantum models. Readers will learn about the Kolmogorov probability theory and its implications in these two areas. Other topics covered include intuitionistic fuzzy sets (IF-set) limit theorems, individual ergodic theorem and relevant statistical applications (examples from correlation theory and factor analysis in Atanassov intuitionistic fuzzy sets systems, the individual ergodic theorem and the Poincaré recurrence theorem). This book is a useful resource for mathematics students and researchers seeking information about fuzzy sets in quantum spaces.

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