Invariant states and a conditional fixed point property for affine actions.
Invariant states for positive operator semigroups
Local and Global Splittings in the State Space of a JB-Algebra.
Long-Time Asymptotic Properties of Dynamical Semigroups on W*-algebras.
On certain properties of the relative entropy of states of operator algebras.
On the Lebesgue decomposition of the normal states of a JBW-algebra
In this article, a theorem is proved asserting that any linear functional defined on a JBW-algebra admits a Lebesque decomposition with respect to any normal state defined on the algebra. Then we show that the positivity (and the unicity) of this decomposition is insured for the trace states defined on the algebra. In fact, this property can be used to give a new characterization of the trace states amoungst all the normal states.
Open projections in operator algebras II: Compact projections
We generalize some aspects of the theory of compact projections relative to a C*-algebra, to the setting of more general algebras. Our main result is that compact projections are the decreasing limits of 'peak projections', and in the separable case compact projections are just the peak projections. We also establish new forms of the noncommutative Urysohn lemma relative to an operator algebra, and we show that a projection is compact iff the associated face in the state space of the algebra is...
Orthogonal Forms and Probability in von Neumann Algebras.
Orthogonal vector measures on projection lattices in a Hilbert space
Positive maps of the CCR algebra with a finite number of non-zero truncated functions
Pure Jauch-Piron states on von Neumann algebras
Pure States and P-Commutative Banach *-Algebras.
Pure states on Jordan algebras
We prove that a pure state on a -algebras or a JB algebra is a unique extension of some pure state on a singly generated subalgebra if and only if its left kernel has a countable approximative unit. In particular, any pure state on a separable JB algebra is uniquely determined by some singly generated subalgebra. By contrast, only normal pure states on JBW algebras are determined by singly generated subalgebras, which provides a new characterization of normal pure states. As an application we contribute...
Quantum ultrametrics on AF algebras and the Gromov-Hausdorff propinquity
We construct quantum metric structures on unital AF algebras with a faithful tracial state, and prove that for such metrics, AF algebras are limits of their defining inductive sequences of finite-dimensional C*-algebras for the quantum propinquity. We then study the geometry, for the quantum propinquity, of three natural classes of AF algebras equipped with our quantum metrics: the UHF algebras, the Effrös-Shen AF algebras associated with continued fraction expansions of irrationals, and the Cantor...
Relatively 'closable' states on C*-algebras.
Remarks on joint distributions of observables
Solution of the factorial Stone-Weierstrass conjecture. An application of the theory of standard split W*-inclusions.
States and representations of CQ*-algebras
Statistical independence of operator algebras
Supporting sequences of pure states on JB algebras
We show that any sequence of mutually orthogonal pure states on a JB algebra A such that forms an almost discrete sequence in the relative topology induced by the primitive ideal space of A admits a sequence consisting of positive, norm one, elements of A with pairwise orthogonal supports which is supporting for in the sense of for all n. Moreover, if A is separable then can be taken such that is uniquely determined by the biorthogonality condition . Consequences of this result improving...