2019
Том 71
№ 11

# Popovich S. V.

Articles: 3
Article (Russian)

### On Homomorphisms of Algebras Generated by Projectors and Coxeter Functors

Ukr. Mat. Zh. - 2003. - 55, № 9. - pp. 1224-1237

We consider algebras generated by idempotents in Banach spaces and orthoprojectors in Hilbert spaces whose sum is a multiple of the identity. We construct several functors generated by homomorphisms of the algebras considered between categories of representations. We investigate properties of these functors and present their applications.

Article (Ukrainian)

### $C*$-Algebras Associated with $F_{2^n }$ Unimodal Dynamical Systems

Ukr. Mat. Zh. - 2001. - 53, № 7. - pp. 929-938

We consider $C*$-algebras associated with simple unimodal one-dimensional ambiguous dynamical systems $(f,R)$ with certain special restrictions. For these algebras, we present a complete classification of irreducible representations in Hilbert spaces and describe the dual space. As an example, we consider the one-parameter family $f_{μ}(x) = μx(1 − x)$.

Article (Russian)