Regularity of domains of parameterized families of closed linear operators
Teresa Winiarska ; Tadeusz Winiarski
Annales Polonici Mathematici, Tome 81 (2003), p. 231-241 / Harvested from The Polish Digital Mathematics Library
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The purpose of this paper is to provide a method of reduction of some problems concerning families At=(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 (Ψt)t∈ of automorphisms of a given Banach space X having two properties: (i) the mapping t↦Ψt is sufficiently regular and (ii) Ψt()=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.

Publié le : 2003-01-01
EUDML-ID : urn:eudml:doc:280339 
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     journal = {Annales Polonici Mathematici},
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     year = {2003},
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Teresa Winiarska; Tadeusz Winiarski. Regularity of domains of parameterized families of closed linear operators. Annales Polonici Mathematici, Tome 81 (2003) pp. 231-241. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap80-0-21/