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The purpose of this paper is to provide a method of reduction of some problems concerning families $A_t = (A(t))_{t∈𝓣}$ of linear operators with domains $(𝓓_t)_{t∈𝓣}$ to a problem in which all the operators have the same domain 𝓓. To do it we propose to construct a family $(Ψ_t)_{t∈𝓣}$ of automorphisms of a given Banach space X having two properties: (i) the mapping $t ↦ Ψ_t$ is sufficiently regular and (ii) $Ψ_t(𝓓) = 𝓓_t$ for t ∈ 𝓣. Three effective constructions are presented: for elliptic operators of second order with the Robin boundary condition with a parameter; for operators in a Hilbert space for which eigenspaces form a complete orthogonal system of closed linear subspaces; and for a class of closed operators having bounded inverses.
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Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
231-241
Opis fizyczny
Daty
wydano
2003
Twórcy
autor
- Teresa Winiarska, Institute of Mathematics, Technical University of Kraków, Warszawska 24, 31-155 Kraków, Poland
autor
- Tadeusz Winiarski, Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
Bibliografia
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_4064-ap80-0-21