Related papers: Toeplitz CAR flows and type I factorizations
We introduce a new construction of $E_0$-semigroups, called generalized CCR flows, with two kinds of descriptions: those arising from sum systems and those arising from pairs of $C_0$-semigroups. We get a new necessary and sufficient…
In this paper using one of the necessary conditions obtained for extendability in [BISSar], we prove that the CAR flows ([Amo01]) on type III factors arising from most quasi-free states are not extendable. As a consequence we find the super…
To a Toeplitz flow $(X,T)$ we associate an ordered $K^0$-group, denoted $K^0(X,T)$, which is order isomorphic to the $K^0$-group of the associated (non-commutative) $C^\ast$-crossed product $C(X)\rtimes_T \mathbb{Z}$. However, $K^0(X,T)$…
We introduce a cohomology theory for spatial super- product systems and compute the $2-$cocycles for some basic examples called as Clifford super-product systems, thereby distinguish them up to isomorphism. This consequently proves that a…
Let $(X,G)$ be a minimal equicontinuous dynamical system, where $X$ is a compact metric space and $G$ some topological group acting on $X$. Under very mild assumptions, we show that the class of regular almost automorphic extensions of…
In this paper we study modular extendability and equimodularity of endomorphisms and E$_0$-semigroups on factors with respect to f.n.s. weights. We show that modular extendability is a property that does not depend on the choice of weights,…
W. Arveson has described a cocycle conjugacy class $U(\alpha)$ of $E_0$-semigroup $\alpha$ on B(H) which is a factor of type $\rm I$. Under some conditions on $\alpha$, there is a $E_0$-semigroup $\beta \in U(\alpha)$ being a flow of shifts…
We investigate $E_0-$semigroups on general factors, which are not necessarily of type I, and analyse associated invariants like product systems, super product systems etc. By tensoring $E_0-$semigroups on type I factors with…
Given an ergodic probability preserving flow $T=(T_t)_{t\in\Bbb R}$, let $I(T):=\{s\in\Bbb R^*\mid T\text{is isomorphic to}(T_{st})_{t\in\Bbb R}\}$. A weakly mixing Gaussian flow $T$ is constructed such that $I(T)$ is uncountable and…
We investigate minimal bounded speedups of Toeplitz flows. We demonstrate that the minimal bounded speedup of a Toeplitz flow need not be another Toeplitz flow and describe techniques for determining whether the resulting speedup is…
Generalizing a construction of A. Weil, we introduce a topological invariant for flows on compact, connected, finite dimensional, abelian, topological groups. We calculate this invariant for some examples and compare the invariant with…
We initiate a study of E-semigroups over convex cones. We prove a structure theorem for E-semigroups which leave the algebra of compact operators invariant. Then we study in detail the CCR flows, E$_0$semigroups constructed from isometric…
We will introduce the Rohlin property for flows on von Neumann algebras and classify them up to strong cocycle conjugacy. This result provides alternative approaches to some preceding results such as Kawahigashi's classification of flows on…
We show that binary Toeplitz flows can be interpreted as Delone dynamical systems induced by model sets and analyse the quantitative relations between the respective system parameters. This has a number of immediate consequences for the…
For each countable residually finite group $G$, we present examples of irregular Toeplitz subshifts in $\{0,1\}^G$ that are topo-isomorphic extensions of its maximal equicontinuous factor. To achieve this, we first establish sufficient…
We prove that many, but not all injective factors arise as crossed products by nonsingular Bernoulli actions of the group $\mathbb{Z}$. We obtain this result by proving a completely general result on the ergodicity, type and Krieger's…
We give in this paper a new construction of factors of type ${\rm III_1}$. Under certain assumptions, we can, thanks to a result by Popa, give a complete classification for this family of factors. Although these factors are never full, we…
We give an easy proof to show that every complex normal Toeplitz matrix is classified as either of type I or of type II. Instead of difference equations on elements in the matrix used in past studies, polynomial equations with coefficients…
We compute an explicit representation of the (topological) automorphism group or a particular Toeplitz subshift. The automorphism group is a (non-finitely generated) subgroup of rational numbers under addition and the shift map corresponds…
Let $P$ be a pointed, closed convex cone in $\mathbb{R}^d$. We prove that for two pure isometric representations $V^{(1)}$ and $V^{(2)}$ of $P$, the associated CAR flows $\beta^{V^{(1)}}$ and $\beta^{V^{(2)}}$ are cocycle conjugate if and…