Regularity of domains of parameterized families of closed linear operators

• Autorzy: Teresa Winiarska , Tadeusz Winiarski
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
• 42C99: None of the above, but in this section
• 35J25: Boundary value problems for second-order elliptic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2003
• Tom: 80
• Numer: 1
• Strony: 231-241

Daty

wydano

2003

Twórcy

autor

Teresa Winiarska

• Teresa Winiarska, Institute of Mathematics, Technical University of Kraków, Warszawska 24, 31-155 Kraków, Poland

autor

Tadeusz Winiarski

• Tadeusz Winiarski, Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Identyfikatory

DOI

10.4064/ap80-0-21