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Regularity of domains of parameterized families of closed linear operators

Teresa Winiarska, Tadeusz Winiarski (2003)

Annales Polonici Mathematici

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;...

Relatively open operators and the ubiquitous concept.

R. W. Cross (1994)

Publicacions Matemàtiques

A linear operator T: D(T) ⊂ X → Y, when X and Y are normed spaces, is called ubiquitously open (UO) if every infinite dimensional subspace M of D(T) contains another such subspace N for which T|N is open (in the relative sense). The following properties are shown to be equivalent: (i) T is UO, (ii) T is ubiquitously almost open, (iii) no infinite dimensional restriction of T is injective and precompact, (iv) either T is upper semi-Fredholm or T has finite dimensional range, (v) for each infinite...

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