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Izv. RAN. Ser. Mat., 2009, Volume 73, Issue 5, Pages 67–82 (Mi izv2713)  

This article is cited in 2 scientific papers (total in 2 papers)

On the factorization of integral operators on spaces of summable functions

N. B. Engibaryan

Institute of Mathematics, National Academy of Sciences of Armenia

Abstract: We consider the factorization $I-K=(I-U^+)(I-U^-)$, where $I$ is the identity operator, $K$ is an integral operator acting on some Banach space of functions summable with respect to a measure $\mu$ on $(a,b)\subset(-\infty,+\infty)$ continuous relative to the Lebesgue measure,
\begin{equation*} (Kf)(x)=\int^b_ak(x,t)f(t)\mu(dt),\qquad x\in(a,b), \end{equation*}
and $U^\pm$ are the desired Volterra operators. A necessary and sufficient condition is found for the existence of this factorization for a rather wide class of operators $K$ with positive kernels and for Hilbert–Schmidt operators.

Keywords: functions summable with respect to a measure, integral operators, Volterra factorization.

DOI: https://doi.org/10.4213/im2713

Full text: PDF file (538 kB)
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English version:
Izvestiya: Mathematics, 2009, 73:5, 921–937

Bibliographic databases:

UDC: 517.9
MSC: 45B05, 45D05, 45E05, 45E10, 45G10, 45P05, 47A68, 47B35, 47G10, 60J10
Received: 02.08.2007

Citation: N. B. Engibaryan, “On the factorization of integral operators on spaces of summable functions”, Izv. RAN. Ser. Mat., 73:5 (2009), 67–82; Izv. Math., 73:5 (2009), 921–937

Citation in format AMSBIB
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\pages 921--937
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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. N. B. Engibaryan, “Differential equations where the derivative is taken with respect to a measure”, Sb. Math., 202:2 (2011), 243–256  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Yengibaryan B.N., Yengibaryan N.B., “On Compactness of Regular Integral Operators in the Space l-1”, J. Contemp. Math. Anal.-Armen. Aca., 53:6 (2018), 317–320  crossref  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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