S. V. Popovych

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Articles: 5

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

Stanislav Popovych

↓ Abstract   |   Article (.pdf)

MFAT 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.

S. A. Kruglyak, S. V. Popovych, Yuriĭ Samoĭlenko

MFAT 11 (2005), no. 4, 383-396


Monomial ∗-algebras and Tapper's conjecture

Stanislav V. Popovych

MFAT 8 (2002), no. 1, 70-74


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

Stanislav Popovych

MFAT 5 (1999), no. 3, 40-48


Unbounded Idempotents

Stanislav Popovych

MFAT 5 (1999), no. 1, 95-103


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