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Funktsional'nyi Analiz i ego Prilozheniya, 2004, Volume 38, Issue 2, Pages 91–94
DOI: https://doi.org/10.4213/faa112 (Mi faa112) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Brief communications

When Is a Sum of Partial Reflections Equal to a Scalar Operator?

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

Institute of Mathematics, Ukrainian National Academy of Sciences
Full-text PDF (157 kB) Citations (7)
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DOI: https://doi.org/10.4213/faa112
Abstract: We describe the set $\widetilde{W}_n$ of values of the parameter $\alpha\in\mathbb{R}$ for which there exists a Hilbert space $H$ and $n$ partial reflections $A_1,\dots,A_n$ (self-adjoint operators such that $A_k^3=A_k$ or, which is the same, self-adjoint operators whose spectra belong to the set $\{-1,0,1\}$) whose sum is equal to the scalar operator $\alpha I_H$.
Keywords: projection, reflection, partial reflection, self-adjoint operator, *-representation.
Received: 12.02.2003
English version:
Functional Analysis and Its Applications, 2004, Volume 38, Issue 2, Pages 157–160
DOI: https://doi.org/10.1023/B:FAIA.0000034047.27498.51
Bibliographic databases:
Document Type: Article
UDC: 517.98
Language: Russian
Citation: A. S. Mellit, V. I. Rabanovich, Yu. S. Samoilenko, “When Is a Sum of Partial Reflections Equal to a Scalar Operator?”, Funktsional. Anal. i Prilozhen., 38:2 (2004), 91–94; Funct. Anal. Appl., 38:2 (2004), 157–160
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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