An application of the Sakai's theorem to the characterization of - algebras.
Central extension of mappings on von Neumann algebras.
Commutators and generators II.
Continuous spatial semigroups of completely positive maps of .
Ergodic Dilation of a Quantum Dynamical System
Using the Nagy dilation of linear contractions on Hilbert space and the Stinespring’s theorem for completely positive maps, we prove that any quantum dynamical system admits a dilation in the sense of Muhly and Solel which satisfies the same ergodic properties of the original quantum dynamical system.
Fixed points and stability of the Cauchy functional equation in -algebras.
Homomorphisms and derivations in -algebras.
How to solve an operator equation.
This article summarizes a series of lectures delivered at the Mathematics Department of the University of Leipzig, Germany, in April 1991, which were to overview techniques for solving operator equations on C*-algebras connected with methods developed in a Spanish-German research project on "Structure and Applications of C*-Algebras of Quotients" (SACQ). One of the researchers in this project was Professor Pere Menal until his unexpected death this April. To his memory this paper shall be dedicated....
Nonlinear Lie-type derivations of von Neumann algebras and related topics
Motivated by the powerful and elegant works of Miers (1971, 1973, 1978) we mainly study nonlinear Lie-type derivations of von Neumann algebras. Let 𝓐 be a von Neumann algebra without abelian central summands of type I₁. It is shown that every nonlinear Lie n-derivation of 𝓐 has the standard form, that is, can be expressed as a sum of an additive derivation and a central-valued mapping which annihilates each (n-1)th commutator of 𝓐. Several potential research topics related to our work are also...
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...
On Cartan Homotopy Formulas in Cyclic Homology.
On Jordan *-derivations and an application
On local derivations in the Kadison sense
Let k be a field. We prove that any polynomial ring over k is a Kadison algebra if and only if k is infinite. Moreover, we present some new examples of Kadison algebras and examples of algebras which are not Kadison algebras.
On the structure of Jordan *-derivations
On the transient and recurrent parts of a quantum Markov semigroup
We define the transient and recurrent parts of a quantum Markov semigroup 𝓣 on a von Neumann algebra 𝓐 and we show that, when 𝓐 is σ-finite, we can write 𝓣 as the sum of such semigroups. Moreover, if 𝓣 is the countable direct sum of irreducible semigroups each with a unique faithful normal invariant state ρₙ, we find conditions under which any normal invariant state is a convex combination of ρₙ's.
Operators preserving ideals in C*-algebras
The aim of this paper is to prove that derivations of a C*-algebra A can be characterized in the space of all linear continuous operators T : A → A by the conditions T(1) = 0, T(L∩R) ⊂ L + R for any closed left ideal L and right ideal R. As a corollary we get an extension of the result of Kadison [5] on local derivations in W*-algebras. Stronger results of this kind are proved under some additional conditions on the cohomologies of A.
Quantum stochastic dynamics on type III factors
Representational indices of derivations of C*-algebras and representations of *-algebras on Krein spaces.
Riesz transforms on generalized Heisenberg groups and Riesz transforms associated to the Cheat flow.
Stability of the Cauchy-Jensen functional equation in -algebras: a fixed point approach.