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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Stability of weighted point evaluation functionals


Authors: Jesús Araujo and Juan J. Font
Journal: Proc. Amer. Math. Soc. 138 (2010), 3163-3170
MSC (2010): Primary 47B38; Secondary 46J10, 47B33
Published electronically: May 12, 2010
MathSciNet review: 2653941
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Abstract: Given $ \epsilon >0$, a continuous linear functional $ \varphi$ on $ C(X)$ is said to be $ \epsilon$-disjointness preserving if $ \left\vert\varphi(f)\varphi(g)\right\vert\le\epsilon$ whenever $ f,g\in C(X)$ satisfy $ \left\Vert f\right\Vert _{\infty} =\left\Vert g\right\Vert _{\infty} =1$ and $ fg\equiv 0$. In this paper we provide the exact maximal distance from $ \epsilon$-disjointness preserving linear functionals to the set of weighted point evaluation functionals.


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Additional Information

Jesús Araujo
Affiliation: Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, Avda. de los Castros, s.n., E-39071 Santander, Spain
Email: araujoj@unican.es

Juan J. Font
Affiliation: Departamento de Matemáticas, Universitat Jaume I, Campus Riu Sec, 8029 AP, Castellón, Spain
Email: font@mat.uji.es

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10214-7
PII: S 0002-9939(10)10214-7
Received by editor(s): June 15, 2009
Received by editor(s) in revised form: September 17, 2009
Published electronically: May 12, 2010
Additional Notes: Research of the first author was partially supported by the Spanish Ministry of Science and Education (Grant number MTM2006-14786).
Research of the second author was partially supported by the Spanish Ministry of Science and Education (Grant number MTM2008-04599) and by Bancaixa (Projecte P1-1B2008-26).
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2010 American Mathematical Society