Characterization of the *-subalgebras in the algebra of bounded operators acting on Hilbert space is presented. Sufficient conditions for the existence of a faithful representation in pre-Hilbert… (More)

We give a modification of I. Klep and M. Schweighofer algebraic reformulation of Connes’ embedding problem by considering ∗-algebra of the countably generated free group. This allows to consider only… (More)

Studying Jone’s polynomials in node theories, their generalization and their connections with ”vertex models” in two-dimensional statistical mechanics, Witten presents Hoph algebra deformations of… (More)

Application of the twisted generalized Weyl construction to description of irreducible representations of the algebra generated by two idempotents and a family of gradedcommuting selfadjoint unitary… (More)

We study the question when for a given ∗-algebra A a sequence of cones Cn ∈ Mn(A) can be realized as cones of positive operators in a faithful ∗-representation of A on a Hilbert space. A… (More)

In this paper we consider enveloping C *-algebras of *-algebras given by generators and defining relations of the following form A = CX, X * | XX * = f (X * X), where f is a Hermitian mapping. Some… (More)

We consider the class of non-commutative ∗-algebras which are path algebras of doubles of quivers with the natural involutions. We study the problem of extending positive truncated functionals on… (More)

We study a mathematical model of a single neuron with self-coupling. The model is based on the FitzHugh-Nagumo oscillator and an equation describing synaptic properties of the neuron. The analysis of… (More)

The Spectral Problem is to describe possible spectra σ(Aj) for an irreducible n-tuple of Hermitian operators s.t. A1 + . . . + An is a scalar operator. In case when mj = |σ(Aj)| are finite and a… (More)

In this paper we consider C∗-algebras connected with a simple unimodal non-bijective dynamical system (f, I) with zero Schwarzian. We associate with f a C∗-algebra C∗(Af ). In the first part we… (More)