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On a Class of Operator Equations in Locally Convex Spaces

Authors
  • Mishin, S. N.1
  • 1 Orel State University named after I. S. Turgenev, ul. Komsomol’skaya 95, Oryol, 302026, Russia , Oryol (Russia)
Type
Published Article
Journal
Russian Mathematics
Publisher
Pleiades Publishing
Publication Date
Nov 29, 2018
Volume
62
Issue
11
Pages
28–44
Identifiers
DOI: 10.3103/S1066369X1811004X
Source
Springer Nature
Keywords
License
Yellow

Abstract

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.

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