scholarly journals Subadditive measure on projectors of von neumann algebra

2020 ◽  
Vol 3 (1) ◽  
pp. 26-28
Author(s):  
Komiljon Kodirov ◽  
Yuldoshali Yigitaliev
Keyword(s):  
Von Neumann Algebra ◽  
Von Neumann ◽  
Orthogonal Projectors

In the paper subadditive measure on the lattice of orthogonal projectors of von Neumann algebra is considered. The basic peoperties of the subadditive measure are estabelished and proved.

scholarly journals Local rigidity for actions of Kazhdan groups on noncommutative Lp-spaces

2015 ◽  
Vol 26 (08) ◽  
pp. 1550064
Author(s):  
Bachir Bekka
Keyword(s):  
Von Neumann Algebra ◽  
Regular Representation ◽  
Von Neumann ◽  
Lp Spaces ◽  
Local Rigidity ◽  
Left Regular Representation ◽  
Left Regular ◽  
Property T ◽  
Finite Factor ◽  
Finite Index Subgroup

Let Γ be a discrete group and 𝒩 a finite factor, and assume that both have Kazhdan's Property (T). For p ∈ [1, +∞), p ≠ 2, let π : Γ →O(Lp(𝒩)) be a homomorphism to the group O(Lp(𝒩)) of linear bijective isometries of the Lp-space of 𝒩. There are two actions πl and πr of a finite index subgroup Γ+ of Γ by automorphisms of 𝒩 associated to π and given by πl(g)x = (π(g) 1)*π(g)(x) and πr(g)x = π(g)(x)(π(g) 1)* for g ∈ Γ+ and x ∈ 𝒩. Assume that πl and πr are ergodic. We prove that π is locally rigid, that is, the orbit of π under O(Lp(𝒩)) is open in Hom (Γ, O(Lp(𝒩))). As a corollary, we obtain that, if moreover Γ is an ICC group, then the embedding g ↦ Ad (λ(g)) is locally rigid in O(Lp(𝒩(Γ))), where 𝒩(Γ) is the von Neumann algebra generated by the left regular representation λ of Γ.

scholarly journals Remarks on positive cones associated with a von Neumann algebra

1981 ◽  
Vol 33 (4) ◽  
pp. 587-591 ◽  
Author(s):  
Hideki Kosaki
Keyword(s):  
Von Neumann Algebra ◽  
Von Neumann

scholarly journals ON PRODUCT SYSTEMS ARISING FROM SUM SYSTEMS

2005 ◽  
Vol 08 (01) ◽  
pp. 1-31 ◽  
Author(s):  
B. V. RAJARAMA BHAT ◽  
R. SRINIVASAN
Keyword(s):  
Hilbert Spaces ◽  
Von Neumann Algebra ◽  
Type I ◽  
Product System ◽  
Von Neumann ◽  
Type Iii ◽  
Product Systems ◽  
Weyl Representation ◽  
Uncountable Family ◽  
Type Spaces

B. Tsirelson constructed an uncountable family of type III product systems of Hilbert spaces through the theory of Gaussian spaces, measure type spaces and "slightly colored noises", using techniques from probability theory. Here we take a purely functional analytic approach and try to have a better understanding of Tsireleson's construction and his examples. We prove an extension of Shale's theorem connecting symplectic group and Weyl representation. We show that the "Shale map" respects compositions (this settles an old conjecture of K. R. Parthasarathy8). Using this we associate a product system to a sum system. This construction includes the exponential product system of Arveson, as a trivial case, and the type III examples of Tsirelson. By associating a von Neumann algebra to every "elementary set" in [0, 1], in a much simpler and direct way, we arrive at the invariants of the product system introduced by Tsirelson, given in terms of the sum system. Then we introduce a notion of divisibility for a sum system, and prove that the examples of Tsirelson are divisible. It is shown that only type I and type III product systems arise out of divisible sum systems. Finally, we give a sufficient condition for a divisible sum system to give rise to a unitless (type III) product system.

*-algebras of unbounded operators affiliated with a von Neumann algebra

2007 ◽  
Vol 140 (3) ◽  
pp. 445-451 ◽  
Author(s):  
M. A. Muratov ◽  
V. I. Chilin
Keyword(s):  
Von Neumann Algebra ◽  
Unbounded Operators ◽  
Von Neumann

$\ell _2$-strictly singular operators on the predual of a hyperfinite von Neumann algebra

2021 ◽  
pp. 1
Author(s):  
Jinghao Huang ◽  
Marat Pliev ◽  
Fedor Sukochev
Keyword(s):  
Von Neumann Algebra ◽  
Von Neumann ◽  
Singular Operators ◽  
Strictly Singular

Inequalities for eigenvalues of sums in a von Neumann algebra

2001 ◽  
pp. 113-126 ◽  
Author(s):  
Hari Bercovici ◽  
Wing Suet Li
Keyword(s):  
Von Neumann Algebra ◽  
Von Neumann

A Class of Measurable Sets Associated with a Von Neumann Algebra

1972 ◽  
Vol s2-5 (1) ◽  
pp. 123-126 ◽  
Author(s):  
G. de Barra
Keyword(s):  
Von Neumann Algebra ◽  
Von Neumann
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