Non-commutative symmetric Markov semigroups.
Non-trivial derivations on commutative regular algebras.
Necessary and sufficient conditions are given for a (complete) commutative algebra that is regular in the sense of von Neumann to have a non-zero derivation. In particular, it is shown that there exist non-zero derivations on the algebra L(M) of all measurable operators affiliated with a commutative von Neumann algebra M, whose Boolean algebra of projections is not atomic. Such derivations are not continuous with respect to measure convergence. In the classical setting of the algebra S[0,1] of all...
Note on a construction of unbounded measures on a nonseparable Hilbert space quantum logic
On measure for projectors
An example of a finite set of projectors in is exhibited for which no 0-1 measure exists.
On measure for projectors. II
On basic concepts of non-commutative topology
On ergodic properties of convolution operators associated with compact quantum groups
Recent results of M. Junge and Q. Xu on the ergodic properties of the averages of kernels in noncommutative -spaces are applied to the analysis of almost uniform convergence of operators induced by convolutions on compact quantum groups.
On homomorphisms of projective lattices in complex Hilbert spaces
On individual subsequential ergodic theorem in von Neumann algebras
We use a non-commutative generalization of the Banach Principle to show that the classical individual ergodic theorem for subsequences generated by means of uniform sequences can be extended to the von Neumann algebra setting.
On limits of -norms of linear operators
On stability properties of positive contractions of L¹-spaces associated with finite von Neumann algebras
We extend the notion of Dobrushin coefficient of ergodicity to positive contractions defined on the L¹-space associated with a finite von Neumann algebra, and in terms of this coefficient we prove stability results for L¹-contractions.
On the Choquet and Bishop-de Leeuw theorems
On the convergence of operators
On the extension problem for unbounded measures on projections
On the Lebesgue decomposition of Gleason measures
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.
Operators from C*-algebras to Banach Spaces.
Order Derivations on Lp-Spaces of W*-Algebras.
Order properties of compact maps on L...-spaces associated with von Neumann algebras.
Orlicz spaces associated with a semi-finite von Neumann algebra
Let be a von Neumann algebra, let be a weight on and let be -function satisfying the -condition. In this paper we study Orlicz spaces, associated with , and .