On a class of operator equations in locally convex spaces

S. N. Mishin

Orel State University named after I.S. Turgenev, 95 Komsomolskaya str., Oryol, 302026 Russia

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. 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.

Keywords: locally convex space, order and type of an operator, characteristic function of an operator.

UDC: 517.983

Received: 06.09.2017

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2018, 62:11, 28–44

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