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Journal of the London Mathematical Society Advance Access originally published online on January 13, 2009
Journal of the London Mathematical Society 2009 79(2):363-376; doi:10.1112/jlms/jdn079
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© 2009 London Mathematical Society

Stability of weighted composition operators between spaces of continuous functions

Jesús Araujo

Departamento MATESCO
Facultad de Ciencias
Universidad de Cantabria
Avda. de los Castros, s. n.
E-39071 Santander
Spain

Juan J. Font

Departamento de Matemáticas
Universitat Jaume I
Campus Riu Sec
8029 AP, Castellón
Spain
font@mat.uji.es

Let {epsilon} > 0. A continuous linear operator T:C(X) -> C(Y) is said to be {epsilon}-disjointness preserving if || (Tf)(Tg)||{infty} ≤ {epsilon} whenever f, g isin C(X) satisfy || f || {infty} = || g||{infty} = 1 and fg {equiv} 0. In this paper we basically address the following question: How close must weighted composition operators be to a given {epsilon}-disjointness preserving operator?

We provide sharp stability bounds.

2000 Mathematics Subject Classification 47B38 (primary), 46J10, 47B33 (secondary).

Research of the first author was partially supported by the Spanish Ministry of Science and Education (Grants numbers MTM2004-02348 and MTM2006-14786). Research of the second author was partially supported by the European Union (FEDER) and the Spanish Ministry of Science and Education (Grant number MTM2008-04599), and by Bancaixa (Projecte P1-1B2008-26).

Received July 8, 2008; revised October 7, 2008; published online January 13, 2009.


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