# Regularity of domains of parameterized families of closed linear operators

Teresa Winiarska; Tadeusz Winiarski

Annales Polonici Mathematici (2003)

- Volume: 80, Issue: 1, page 231-241
- ISSN: 0066-2216

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topTeresa 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 -

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