Regularity of domains of parameterized families of closed linear operators

Teresa Winiarska, and Tadeusz Winiarski. "Regularity of domains of parameterized families of closed linear operators." Annales Polonici Mathematici 80.1 (2003): 231-241. <http://eudml.org/doc/280339>.

@article{TeresaWiniarska2003,
abstract = {The purpose of this paper is to provide a method of reduction of some problems concerning families $A_t = (A(t))_\{t∈\}$ of linear operators with domains $(_t)_\{t∈\}$ to a problem in which all the operators have the same domain . To do it we propose to construct a family $(Ψ_t)_\{t∈\}$ of automorphisms of a given Banach space X having two properties: (i) the mapping $t ↦ Ψ_t$ is sufficiently regular and (ii) $Ψ_t() = _t$ for 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.},
author = {Teresa Winiarska, Tadeusz Winiarski},
journal = {Annales Polonici Mathematici},
keywords = {families of operators; isomorphic domains; elliptic operators of second order; operators in Hilbert spaces; closed operators},
language = {eng},
number = {1},
pages = {231-241},
title = {Regularity of domains of parameterized families of closed linear operators},
url = {http://eudml.org/doc/280339},
volume = {80},
year = {2003},
}

TY - JOUR
AU - Teresa Winiarska
AU - Tadeusz Winiarski
TI - Regularity of domains of parameterized families of closed linear operators
JO - Annales Polonici Mathematici
PY - 2003
VL - 80
IS - 1
SP - 231
EP - 241
AB - The purpose of this paper is to provide a method of reduction of some problems concerning families $A_t = (A(t))_{t∈}$ of linear operators with domains $(_t)_{t∈}$ to a problem in which all the operators have the same domain . To do it we propose to construct a family $(Ψ_t)_{t∈}$ of automorphisms of a given Banach space X having two properties: (i) the mapping $t ↦ Ψ_t$ is sufficiently regular and (ii) $Ψ_t() = _t$ for 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.
LA - eng
KW - families of operators; isomorphic domains; elliptic operators of second order; operators in Hilbert spaces; closed operators
UR - http://eudml.org/doc/280339
ER -