Stability of weighted point evaluation functionals
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- by Jesús Araujo and Juan J. Font PDF
- Proc. Amer. Math. Soc. 138 (2010), 3163-3170 Request permission
Abstract:
Given $\epsilon >0$, a continuous linear functional $\varphi$ on $C(X)$ is said to be $\epsilon$-disjointness preserving if $\left |\varphi (f)\varphi (g)\right |\le \epsilon$ whenever $f,g\in C(X)$ satisfy $\left \|f\right \|_{\infty } =\left \| g\right \|_{\infty } =1$ 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.References
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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
- 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
- © Copyright 2010 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 138 (2010), 3163-3170
- MSC (2010): Primary 47B38; Secondary 46J10, 47B33
- DOI: https://doi.org/10.1090/S0002-9939-10-10214-7
- MathSciNet review: 2653941