This is an announcement for the paper "Stability and instability of weighted composition operators" by Jesus Araujo and Juan J. Font.
Abstract: Let $\epsilon >0$. A continuous linear operator $T:C(X) \ra C(Y)$ is said to be {\em $\epsilon$-disjointness preserving} if $\vc (Tf)(Tg)\vd_{\infty} \le \epsilon$, whenever $f,g\in C(X)$ satisfy $\vc f\vd_{\infty} =\vc g\vd_{\infty} =1$ and $fg\equiv 0$. In this paper we address basically two main questions: 1.- How close there must be a weighted composition operator to a given $\epsilon$-disjointness preserving operator? 2.- How far can the set of weighted composition operators be from a given $\epsilon$-disjointness preserving operator? We address these two questions distinguishing among three cases: $X$ infinite, $X$ finite, and $Y$ a singleton ($\epsilon$-disjointness preserving functionals). We provide sharp stability and instability bounds for the three cases.
Archive classification: math.FA
Mathematics Subject Classification: Primary 47B38; Secondary 46J10, 47B33
Remarks: 37 pages, 7 figures. A beamer presentation at www.araujo.tk
The source file(s), ejemploy0d.eps: 10802 bytes stability86.tex: 91977 bytes total2gabove.eps: 20323 bytes total2i.eps: 20467 bytes w01c.eps: 9921 bytes w11d.eps: 12594 bytes w21d.eps: 12278 bytes z1d.eps: 12984 bytes, is(are) stored in gzipped form as 0801.2532.tar.gz with size 46kb. The corresponding postcript file has gzipped size 180kb.
Submitted from: araujoj@unican.es
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