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March 2011 Histories Distorted by Partial Isometries
Ilwoo Cho
J. Phys. Math. 3: 1-18 (March 2011). DOI: 10.4303/jpm/P110301


In quantum dynamical systems, a history is defined by a pair $(M,\gamma)$, consisting of a type $I$ factor $M$, acting on a Hilbert space $H$, and an $E_0$-group $\gamma = (\gamma_t)_{t\in \Bbb{R}}$, satisfying certain additional conditions. In this paper, we distort a given history $(M,\gamma)$, by a finite family $\mathcal{G}$ of partial isometries on $H$. In particular, such a distortion is dictated by the combinatorial relation on the family $\mathcal{G}$. Two main purposes of this paper are (i) to show the existence of distortions on histories, and (ii) to consider how distortions work. We can understand Sections 3, 4 and 5 as the proof of the existence of distortions (i), and the properties of distortions (ii) are shown in Section 6.


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Ilwoo Cho. "Histories Distorted by Partial Isometries." J. Phys. Math. 3 1 - 18, March 2011.


Published: March 2011
First available in Project Euclid: 29 January 2013

zbMATH: 1264.81207
Digital Object Identifier: 10.4303/jpm/P110301

Primary: 05C21 , 05C25 , 16T20 , 22A22 , 46N50 , 47L15 , 47L75 , 47L90 , 81Q12

Keywords: Associative rings and algebras , Combinatorics For finite fields , Flows in graphs , functional analysis , graph theory , Graphs and abstract algebra , Hopf algebras , Non-selfadjoint operator theory , Operator algebras with symbol structure , operator theory , quantum groups , quantum theory , Ring-theoretic aspects of quantum groups , Topological groupoids , topological groups

Rights: Copyright © 2011 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

Vol.3 • March 2011
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