Range of operators and regularity of solutions
Regular operators on partial inner product spaces
Regularity of domains of parameterized families of closed linear operators
The purpose of this paper is to provide a method of reduction of some problems concerning families of linear operators with domains to a problem in which all the operators have the same domain . To do it we propose to construct a family of automorphisms of a given Banach space X having two properties: (i) the mapping is sufficiently regular and (ii) 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.
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...
Relatively tauberian resolvent operators.
Remark on linear equations in Banach space
Remark on sums of complemented subspaces
Representation and duality of multiplication operators on archimedean Riesz spaces
Representations for the Drazin inverse of bounded operators on Banach space.
Reverse order law for the Moore-Penrose inverse in -algebras.