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Mat. Zametki, 1977, Volume 22, Issue 2, Pages 179–188 (Mi mz8039)  

This article is cited in 4 scientific papers (total in 4 papers)

An asymptotic variant of the Fuglede–Putnam theorem on commutators for elements of Banach algebras

E. A. Gorina, M. I. Karahanyanb

a M. V. Lomonosov Moscow State University
b Yerevan State University

Abstract: The Fuglede–Putnam theorem (in Moore's asymptotic form) on the commutators of normal operators of a Hilbert space is generalized, in particular, in the following form. Let $a_1,a_2,b_1$ and $b_2$ be the elements of a complex Banach algebra such that $[a_1,b_1]=[a_2,b_2]=0$ and $\|e^{\overline\lambda a_1-\lambda b_1}\|=o(|\lambda|^{1/2})$, $\|e^{\overline\lambda a_2-\lambda b_2}\|=o(|\lambda|^{1/2})$ as $\lambda\to\infty$. Then the inequality $\|b_1x-xb_2\|\le\varphi(\|a_1-xa_2\|)$, where $\varphi(\varepsilon)\to0$ as $\varepsilon\to0$, holds uniformly in every ball $\|x\|\le R<\infty$.

Full text: PDF file (786 kB)

English version:
Mathematical Notes, 1977, 22:2, 591–596

Bibliographic databases:

UDC: 513.8
Received: 08.04.1976

Citation: E. A. Gorin, M. I. Karahanyan, “An asymptotic variant of the Fuglede–Putnam theorem on commutators for elements of Banach algebras”, Mat. Zametki, 22:2 (1977), 179–188; Math. Notes, 22:2 (1977), 591–596

Citation in format AMSBIB
\Bibitem{GorKar77}
\by E.~A.~Gorin, M.~I.~Karahanyan
\paper An asymptotic variant of the Fuglede--Putnam theorem on commutators for elements of Banach algebras
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 2
\pages 179--188
\mathnet{http://mi.mathnet.ru/mz8039}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=461138}
\zmath{https://zbmath.org/?q=an:0378.46044}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 2
\pages 591--596
\crossref{https://doi.org/10.1007/BF01780966}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. Karakhanyan, “An Asymptotic Version of General Commutator Theorems”, Funct. Anal. Appl., 39:4 (2005), 311–313  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. M. I. Karahanyan, “On the abstract theorem of Picard”, Lobachevskii J. Math., 18 (2005), 127–130  mathnet  mathscinet  zmath
    3. I. M. Karakhanyan, M. I. Karakhanyan, “O subnormalnosti v banakhovoi algebre”, Uch. zapiski EGU, ser. Fizika i Matematika, 2008, no. 1, 10–17  mathnet
    4. I. M. Karakhanyan, M. I. Karakhanyan, “A remark on asymptotic property of commutators”, Uch. zapiski EGU, ser. Fizika i Matematika, 2009, no. 2, 63–66  mathnet
  • Математические заметки Mathematical Notes
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