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Funktsional'nyi Analiz i ego Prilozheniya, 2002, Volume 36, Issue 3, Pages 20–35
DOI: https://doi.org/10.4213/faa201 (Mi faa201) 		 
This article is cited in 61 scientific papers (total in 61 papers)

On Sums of Projections

S. A. Kruglyak, V. I. Rabanovich, Yu. S. Samoilenko

Institute of Mathematics, Ukrainian National Academy of Sciences
Full-text PDF (257 kB) Citations (61)
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DOI: https://doi.org/10.4213/faa201
Abstract: In the paper, for all $n\in\mathbb{N}$, we describe the set $\Sigma_n$ of all real numbers $\alpha$ admitting a collection of projections $P_1,\dots,P_n$ on a Hilbert space $H$ such that $\sum_{k=1}^n P_k=\alpha I$ ($I$ is the identity operator on $H$) and study the problem to find all collections of this kind for a given $\alpha\in\Sigma_n$.
Keywords: algebra, representation, operator, matrix, projection, identity.
Received: 08.11.2001
English version:
Functional Analysis and Its Applications, 2006, Volume 36, Issue 3, Pages 182–195
DOI: https://doi.org/10.1023/A:1020193804109
Bibliographic databases:
Document Type: Article
UDC: 517.98
Language: Russian
Citation: S. A. Kruglyak, V. I. Rabanovich, Yu. S. Samoilenko, “On Sums of Projections”, Funktsional. Anal. i Prilozhen., 36:3 (2002), 20–35; Funct. Anal. Appl., 36:3 (2006), 182–195
Citation in format AMSBIB
\Bibitem{KruRabSam02}
\by S.~A.~Kruglyak, V.~I.~Rabanovich, Yu.~S.~Samoilenko
\paper On Sums of Projections
\jour Funktsional. Anal. i Prilozhen.
\yr 2002
\vol 36
\issue 3
\pages 20--35
\mathnet{http://mi.mathnet.ru/faa201}
\crossref{https://doi.org/10.4213/faa201}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1935900}
\zmath{https://zbmath.org/?q=an:1038.47001}
\transl
\jour Funct. Anal. Appl.
\yr 2006
\vol 36
\issue 3
\pages 182--195
\crossref{https://doi.org/10.1023/A:1020193804109}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0036377329}
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    • This publication is cited in the following 61 articles:
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
     
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