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On a transformation of integral equations. (English. Russian original) Zbl 1390.45004
J. Contemp. Math. Anal., Armen. Acad. Sci. 52, No. 6, 288-294 (2017); translation from Izv. Nats. Akad. Nauk Armen., Mat. 52, No. 6, 3-11 (2017).
Summary: Let $$E = E(a,b)$$ be some Banach space of measurable functions on $$(a,b)$$, $$I$$ be the identity operator, and let $$\hat K$$ be a Fredholm-type regular integral operator acting on $$E$$ and $$\hat{K}_\pm$$ be its triangular parts. We consider the representation $$I - \hat K = \left( {I - {{\hat K}_ - }} \right)\left( {I - \hat U} \right)\left( {I - {{\hat K}_ + }} \right)$$, for some known classes of integral operators. In particular,we show that under certain conditions the operator $$\hat U$$ is positive and its spectral radius satisfies the condition $$r\left( {\hat U} \right) < 1$$. Also, we give some possible applications of the representation.
##### MSC:
 45A05 Linear integral equations
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