Russian Mathematics

, Volume 62, Issue 11, pp 28–44 | Cite as

On a Class of Operator Equations in Locally Convex Spaces

  • S. N. MishinEmail author


We consider a general method of solving equations whose left-hand side is a series by powers of a linear continuous operator acting in a locally convex space. Obtained solutions are given by operator series by powers of the same operator as the left-hand side of the equation. The research is realized by means of characteristics (of order and type) of operator as well as operator characteristics (of operator order and operator type) of vector relatively of an operator. In research we also use a convergence of operator series on equicontinuous bornology.


locally convex space order and type of an operator characteristic function of an operator 


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© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Orel State University named after I. S. TurgenevOryolRussia

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