arXiv subjects
Publications and source records attributed to Alexander Pavlov.
Analogues for Hilbert C*-modules of classical results of Fourier series theory in Hilbert spaces are considered. Relations between different properties of orthogonal and orthonormal systems for Hilbert C*-modules are studied with special attention paid on the differences with the well-known Hilbert space situation.
This paper deals with a "naive" way of generalization of the Kazhdan's property (T) to C*-algebras. This approach differs from the approach of Connes and Jones, which has already demonstrated its utility. Nevertheless it turned out that our approach is applicable to the following rather subtle question in the theory of C*-Hilbert modules. We prove that a separable unital C*-algebra A has property MI (module-infinite, i.e., any C*-Hilbert module over A is self-dual if and only if it is finitely generated projective) if and only if it has not property (T1P) (property (T) at one point}, i.e. there exists in the unitary dual of A a finite dimensional isolated point. The commutative case was studied in a previous paper.
An algebraic procedure of getting of canonical variables in a rigid body dynamics is presented. The method is based on using a structure of an algebra of Lie-Poisson brackets with which a Hamiltonian dynamics is set. In a particular case of a problem of a top in a homogeneous gravitation field the method leads to well-known Andoyer-Deprit variables. Earlier, the method of getting of them was based on geometric approach.