Search results for "Linear extension"
showing 4 items of 4 documents
On linear extension operators from growths of compactifications of products
1996
Abstract We obtain some results on product spaces. Among them we prove that for noncompact spaces X 1 and X 2 , the norm of every linear extension operator from C ( β ( X 1 × X 2 ) β ( X 1 × X 2 )) into C ( β ( X 1 × X 2 )) is greater or equal than 2, and also that β ( X 1 × X 2 ) β ( X 1 × X 2 ) is not a neighborhood retract of β ( X 1 × X 2 ).
On certain linear operators in spaces of ultradifferentiable functions
1996
Let ω be a weight in the sense of Braun, Meise, Taylor, which defines a non-quasianalytic class. Let H be a compact subset of ℝn. It is proved that for every function ƒ on ℝn which belongs to the non-quasianalytic (ω)-class, there is an element g of the same class which is analytic on ℝn\H and such that Dαƒ(x) = Dαg(x) for every x ∈ H and α ∈ ℕ0n. A similar result is proved for functions of the Roumieu type. Continuous linear extension operators of Whitney jets with additional properties are also obtained.
The diamond partial order in rings
2013
In this paper we introduce a new partial order on a ring, namely the diamond partial order. This order is an extension of a partial order defined in a matrix setting in [J.K. Baksalary and J. Hauke, A further algebraic version of Cochran's theorem and matrix partial orderings, Linear Algebra and its Applications, 127, 157--169, 1990]. We characterize the diamond partial order on rings and study its relationships with other partial orders known in the literature. We also analyze successors, predecessors and maximal elements under the diamond order.
Linear extension operators on products of compact spaces
2003
Abstract Let X and Y be the Alexandroff compactifications of the locally compact spaces X and Y , respectively. Denote by Σ( X × Y ) the space of all linear extension operators from C(( X × Y )⧹(X×Y)) to C(( X × Y )) . We prove that X and Y are σ -compact spaces if and only if there exists a T∈Σ( X × Y ) with ‖ T ‖ Γ∈Σ( X × Y ) with ‖ Γ ‖=1. Assuming the existence of a T∈Σ( X × Y ) with ‖ T ‖ X and Y is equivalent to the fact that ‖ Γ ‖⩾2 for every Γ∈Σ( X × Y ) .