# S. V. Popovych

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Articles: 5

### Algebraically admissible cones in free products of $*$-algebras

Stanislav Popovych

Methods Funct. Anal. Topology 16 (2010), no. 1, 51-56

It was proved in~\cite{Pop09b} that a $*$-algebra is $C^*$-representable, i.e., $*$-isomorphic to a self-adjoint subalgebra of bounded operators acting on a Hilbert space if and only if there is an algebraically admissible cone in the real space of Hermitian elements of the algebra such that the algebra unit is an Archimedean order unit. In the present paper we construct such cones in free products of $C^*$-representable $*$-algebras generated by unitaries. We also express the reducing ideal of any algebraically bounded $*$-algebra with corepresentation $\mathcal F/\mathcal J$ where $\mathcal F$ is a free algebra as a closure of the ideal $\mathcal J$ in some universal enveloping $C^*$-algebra.

### The spectral problem and algebras associated with extended Dynkin graphs. I.

Methods Funct. Anal. Topology 11 (2005), no. 4, 383-396

### Monomial ∗-algebras and Tapper's conjecture

Stanislav V. Popovych

Methods Funct. Anal. Topology 8 (2002), no. 1, 70-74

### Conditions for embedding $*$-algebra into $C^{*}$-algebra

Stanislav Popovych

Methods Funct. Anal. Topology 5 (1999), no. 3, 40-48

### Unbounded Idempotents

Stanislav Popovych

Methods Funct. Anal. Topology 5 (1999), no. 1, 95-103