Extensions Of Positive Operators Research Articles

A representation of sup-completion

It was showed by Donner in [Extension of positive operators and Korovkin theorems, Lecture Notes in Mathematics, vol. 904, Springer-Verlag, Berlin-New York, 1982] that every order complete vector lattice X X may be embedded into a cone X s X^s , called the sup-completion of X X . We show that if one represents the universal completion of X X as C ∞ ( K ) C^\infty (K) , then X s X^s is the set of all continuous functions from K K to [ − ∞ , ∞ ] [-\infty ,\infty ] that dominate some element of X X . This provides a functional representation of X s X^s , as well as an easy alternative proof of its existence.

Positive Self-adjoint Operator Extensions with Applications to Differential Operators

In this paper we consider extensions of positive operators. We study the connections between the von Neumann theory of extensions and characterisations of positive extensions via decompositions of the domain of the associated form. We apply the results to elliptic second order differential operators and look in particular at examples of the Laplacian on a disc and the Aharonov–Bohm operator.

Extensions of positive operators and functionals

We consider linear operators defined on a subspace of a complex Banach space into its topological antidual acting positively in a natural sense. The main theorem is a constructive characterization of the bounded positive extendibility of these linear mappings. In this frame we characterize operators with a compact or a closed range extension. As a main application of our general extension theorem, we present some necessary and sufficient conditions for a positive functional defined on a left ideal of a Banach ⁎-algebra to admit a representable positive extension.

Maximal-Valued Extensions of Positive Operators

Maximal-Valued Extensions of Positive Operators

Extensions of positive operators and extreme points. III

Extensions of positive operators and extreme points. III

Extensions of positive operators and extreme points. IV

Extensions of positive operators and extreme points. IV

Extensions of positive operators and extreme points. II

Extensions of positive operators and extreme points. II

Extensions of positive operators and extreme points. I

Extensions of positive operators and extreme points. I

Invariant extensions of positive operators for right amenable semigroups

Invariant extensions of positive operators for right amenable semigroups

Extensions of positive operators between Banach lattices

Extensions of positive operators between Banach lattices