2008/01/16 by Jesus Araujo, Araujo, Jesus, Juan J. Font +1
Mathematics · #47B33 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 47B38 #Secondary 46J10 #math.FA #msc:46J10 #msc:47B33 #msc:47B38
paper · pdf · doi:10.48550/arxiv.0801.2477
37 pages, 7 figures. A beamer presentation at http://www.araujo.tk
arxiv created 2008/01/16 · arxiv updated 2009/12/01
Let ε>0. A continuous linear operator T:C(X) \ra C(Y) is said to be \em ε-disjointness preserving if \vc (Tf)(Tg)\vd∞ ≤ ε, whenever f,g∈ C(X) satisfy \vc f\vd∞ =\vc g\vd∞ =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 ε-disjointness preserving operator? 2.- How far can the set of weighted composition operators be from a given ε-disjointness preserving operator? We address these two questions distinguishing among three cases: X infinite, X finite, and Y a singleton (ε-disjointness preserving functionals). We provide sharp stability and instability bounds for the three cases.