V. I. Rabanovich

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Articles: 5

Some remarks on Hilbert representations of posets

V. Ostrovskyi, S. Rabanovich

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 20 (2014), no. 2, 149–163

For a certain class of finite posets, we prove that all their irreducible orthoscalar representations are finite-dimensional and describe those, for which there exist essential (non-degenerate) irreducible orthoscalar representations.

On decompositions of the identity operator into a linear combination of orthogonal projections

S. Rabanovich, A. A. Yusenko

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 16 (2010), no. 1, 57-68

In this paper we consider decompositions of the identity operator into a linear combination of $k\ge 5$ orthogonal projections with real coefficients. It is shown that if the sum $A$ of the coefficients is closed to an integer number between $2$ and $k-2$ then such a decomposition exists. If the coefficients are almost equal to each other, then the identity can be represented as a linear combination of orthogonal projections for $\frac{k-\sqrt{k^2-4k}}{2} < A < \frac{k+\sqrt{k^2-4k}}{2}$. In the case where some coefficients are sufficiently close to $1$ we find necessary conditions for the existence of the decomposition.

On the decomposition of the identity into a sum of idempotents

T. Ehrhardt, V. Rabanovich, Yu. Samoǐlenko, B. Silbermann

Methods Funct. Anal. Topology 7 (2001), no. 2, 1-6

On representations of $\mathcal F_n$-algebras and invertibility symbols

Slavik Rabanovich, Yuriĭ Samoĭlenko

Methods Funct. Anal. Topology 4 (1998), no. 4, 86-96

Banach algebras generated by three idempotents

V. I. Rabanovitch

Methods Funct. Anal. Topology 4 (1998), no. 1, 65-67


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