scholarly journals Von Neumann algebras generated by two unitary operators u and v with u 2 = v 3 = 1

2017 ◽  
Vol 453 (2) ◽  
pp. 1139-1144
Author(s):  
Zhangsheng Zhu ◽  
Junsheng Fang ◽  
Rui Shi
Keyword(s):  
Von Neumann Algebras ◽  
Unitary Operators ◽  
Von Neumann

scholarly journals THE RELATIVE WEAK ASYMPTOTIC HOMOMORPHISM PROPERTY FOR INCLUSIONS OF FINITE VON NEUMANN ALGEBRAS

2011 ◽  
Vol 22 (07) ◽  
pp. 991-1011 ◽  
Author(s):  
JUNSHENG FANG ◽  
MINGCHU GAO ◽  
ROGER R. SMITH
Keyword(s):  
Finite Number ◽  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
Unitary Operators ◽  
Von Neumann ◽  
The One ◽  
Finite Von Neumann Algebras

A triple of finite von Neumann algebras B ⊆ N ⊆ M is said to have the relative weak asymptotic homomorphism property if there exists a net of unitary operators {uλ}λ∈Λ in B such that [Formula: see text] for all x,y ∈ M. We prove that a triple of finite von Neumann algebras B ⊆ N ⊆ M has the relative weak asymptotic homomorphism property if and only if N contains the set of all x ∈ M such that [Formula: see text] for a finite number of elements x1, …, xn in M. Such an x is called a one-sided quasi-normalizer of B, and the von Neumann algebra generated by all one-sided quasi-normalizers of B is called the one-sided quasi-normalizer algebra of B. We characterize one-sided quasi-normalizer algebras for inclusions of group von Neumann algebras and use this to show that one-sided quasi-normalizer algebras and quasi-normalizer algebras are not equal in general. We also give some applications to inclusions L(H) ⊆ L(G) arising from containments of groups. For example, when L(H) is a masa we determine the unitary normalizer algebra as the von Neumann algebra generated by the normalizers of H in G.

scholarly journals Convex combinations of unitary operators in von Neumann algebras

1986 ◽  
Vol 66 (3) ◽  
pp. 365-380 ◽  
Author(s):  
Catherine L Olsen ◽  
Gert K Pedersen
Keyword(s):  
Von Neumann Algebras ◽  
Unitary Operators ◽  
Von Neumann

scholarly journals Unitary operators in real von Neumann algebras

2012 ◽  
Vol 386 (2) ◽  
pp. 933-938 ◽  
Author(s):  
J.C. Navarro-Pascual ◽  
M.A. Navarro
Keyword(s):  
Von Neumann Algebras ◽  
Unitary Operators ◽  
Von Neumann

Lectures on von Neumann Algebras

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

scholarly journals Approximate Tensorization of the Relative Entropy for Noncommuting Conditional Expectations

2021 ◽  
Author(s):  
Ivan Bardet ◽  
Ángela Capel ◽  
Cambyse Rouzé
Keyword(s):  
Relative Entropy ◽  
Von Neumann Algebras ◽  
Logarithmic Sobolev Inequality ◽  
Spin Systems ◽  
Von Neumann ◽  
Strong Subadditivity ◽  
Finite Dimensional ◽  
Lattice Spin ◽  
Lattice Spin Systems ◽  
Conditional Expectations

AbstractIn this paper, we derive a new generalisation of the strong subadditivity of the entropy to the setting of general conditional expectations onto arbitrary finite-dimensional von Neumann algebras. This generalisation, referred to as approximate tensorization of the relative entropy, consists in a lower bound for the sum of relative entropies between a given density and its respective projections onto two intersecting von Neumann algebras in terms of the relative entropy between the same density and its projection onto an algebra in the intersection, up to multiplicative and additive constants. In particular, our inequality reduces to the so-called quasi-factorization of the entropy for commuting algebras, which is a key step in modern proofs of the logarithmic Sobolev inequality for classical lattice spin systems. We also provide estimates on the constants in terms of conditions of clustering of correlations in the setting of quantum lattice spin systems. Along the way, we show the equivalence between conditional expectations arising from Petz recovery maps and those of general Davies semigroups.

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