On action of diffeomorphisms of C*-algebras on derivations

AbstractIn this paper we consider automorphisms of the domains of closed *-derivations of C*-algebras and show that they extend to automorphisms of C*-algebras, so we call them diffeomorphisms. The diffeomorphisms generate transformations of the sets of closed *-derivations of C*-algebras. In this paper we study the subgroups of diffeomorphisms that define “bounded” shifts of derivations and the subgroups of the stabilizers of derivations

Relations and trails in lattices of projections in W*-algebras

The paper studies HH-relations in the lattices P(M) of all projections of W*-algebras M. If M is a finite algebra, all these relations are generated by trails in P(M). If M is an infinite countably decomposable factor, they are either generated by trails, or associated with them

Clarkson-McCarthy inequalities for l p -spaces of operators in Schatten ideals

In this paper we obtain generalized Clarkson-McCarthy inequalities for spaces lq(Sp) of operators from Schatten ideals Sp. We show that all Clarkson-McCarthy type inequalities are, in fact, some estimates on the norms of operators acting on the spaces lq(Sp) or from one such space into another. We also extend some inequalities for partitioned operators and for Cartesian decomposition of operators

Non-unitary representations of nilpotent groups, I: Cohomologies, extensions and neutral cocycles

Let λbe a finite-dimensional representation of a connected nilpotent group Gand Ube a unitary representation of G. We investigate the structure of the extensions of λby Uand, correspondingly, the group H1(λ, U)of 1-cohomologies. A spectral criterion of triviality of H1(λ, U)is proved and systematically used in the study of various types of decomposition of the extensions. We consider a special type of (λ, U)-cocycles – neutral cocycles, which play a crucial role in the theory of J-unitary representations of groups on Pontryagin Πk-spaces

Representations of nilpotent groups on spaces with indefinite metric

The paper studies the structure of J-unitary representations of connected nilpotent groups on Πk-spaces, that is, the representations on a Hilbert space preserving a quadratic form “with a finite number of negative squares”. Apart from some comparatively simple cases, such representations can be realized as double extensions of finite-dimensional representations by unitary ones. So their study is based on some special cohomological technique. We concentrate mostly on the problems of the decomposition of these representations and the classification of “non-decomposable” ones

On cohomologies and representations of groups with normal Engel subgroups

Let lambda and U be representations of a group G with a normal Engel subgroup N. The paper studies triviality conditions for the cohomology group H1(G; lambda;U) when lambda and U are sectionally spectrally disjoint and examines some decompositions of the extension e(lambda; U; ksi) of lambda by U associated with non-trivial (lambda; U)-cocycles ksi

On representations of groups and algebras in spaces with indefinite metric (in Russian)

The paper contains a survey of results on the structure of J-symmetric algebras of operators in Pontryagin and Krein spaces and also results on representations of groups and algebras in these spaces

Relations and radicals in abstract lattices and in lattices of subspaces of Banach spaces and of ideals of Banach algebras: Amitsur's theory revisited

We refine Amitsur's theory of radicals in complete lattices and apply the obtained results to the theory of radicals in the lattices of subspaces of Banach spaces and in the lattices of ideals of Banach and C*-algebras and of Banach Lie algebras