On the stability index for weighted composition operators
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http://dx.doi.org/10.1016/j.jat.2010.06.006 |
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Title
On the stability index for weighted composition operatorsDate
2010Publisher
ElsevierISSN
219045Bibliographic citation
Journal of Approximation Theory, 162, 12, p. 2136-2148Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/publishedVersionSubject
Abstract
Let ϵ>0. A continuous linear operator T:C(X)⟶C(Y) is said to ϵ-preserve disjointness if ‖(Tf)(Tg)‖∞≤ϵ, whenever f,g∈C(X) satisfy ‖f‖∞=‖g‖∞=1 and fg≡0. In this paper we continue our study of the minimal interval where ... [+]
Let ϵ>0. A continuous linear operator T:C(X)⟶C(Y) is said to ϵ-preserve disjointness if ‖(Tf)(Tg)‖∞≤ϵ, whenever f,g∈C(X) satisfy ‖f‖∞=‖g‖∞=1 and fg≡0. In this paper we continue our study of the minimal interval where the possible maximal distance from a norm one operator which ϵ-preserves disjointness to the set of weighted composition maps may lie. We provide sharp bounds for both the finite and the infinite case, which turn out to be completely different. [-]
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