Stability and Instability of Weighted Composition Operators
نویسندگان
چکیده
Let ǫ > 0. A continuous linear operator T : C(X) −→ C(Y ) is said to be ǫ-disjointness preserving if ‖(Tf)(Tg)‖ ∞ ≤ ǫ, whenever f, g ∈ C(X) satisfy ‖f‖ ∞ = ‖g‖ ∞ = 1 and fg ≡ 0. In this paper we address basically two main questions: 1.How close there must be a weighted composition operator to a given ǫ-disjointness preserving operator? 2.How far can the set of weighted composition operators be from a given ǫ-disjointness preserving operator? We address these two questions distinguishing among three cases: X infinite, X finite, and Y a singleton (ǫ-disjointness preserving functionals). We provide sharp stability and instability bounds for the three cases.
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تاریخ انتشار 2008