Stability of weighted point evaluation functionals
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- by Jesús Araujo and Juan J. Font
- Proc. Amer. Math. Soc. 138 (2010), 3163-3170
- DOI: https://doi.org/10.1090/S0002-9939-10-10214-7
- Published electronically: May 12, 2010
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Abstract:
Given $\epsilon >0$, a continuous linear functional $\varphi$ on $C(X)$ is said to be $\epsilon$-disjointness preserving if $\left |\varphi (f)\varphi (g)\right |\le \epsilon$ 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
- J. Araujo, E. Beckenstein, and L. Narici, Biseparating maps and homeomorphic real-compactifications, J. Math. Anal. Appl. 192 (1995), no. 1, 258–265. MR 1329423, DOI 10.1006/jmaa.1995.1170
- Jesús Araujo and Juan J. Font, Stability of weighted composition operators between spaces of continuous functions, J. Lond. Math. Soc. (2) 79 (2009), no. 2, 363–376. MR 2496519, DOI 10.1112/jlms/jdn079
- J. Araujo and Juan J. Font, On the stability index for weighted composition operators. Preprint.
- Gregor Dolinar, Stability of disjointness preserving mappings, Proc. Amer. Math. Soc. 130 (2002), no. 1, 129–138. MR 1855629, DOI 10.1090/S0002-9939-01-06023-3
- J. J. Font and S. Hernández, On separating maps between locally compact spaces, Arch. Math. (Basel) 63 (1994), no. 2, 158–165. MR 1289298, DOI 10.1007/BF01189890
- Krzysztof Jarosz, Automatic continuity of separating linear isomorphisms, Canad. Math. Bull. 33 (1990), no. 2, 139–144. MR 1060366, DOI 10.4153/CMB-1990-024-2
- Jyh-Shyang Jeang and Ngai-Ching Wong, Weighted composition operators of $C_0(X)$’s, J. Math. Anal. Appl. 201 (1996), no. 3, 981–993. MR 1400575, DOI 10.1006/jmaa.1996.0296
- B. E. Johnson, Approximately multiplicative functionals, J. London Math. Soc. (2) 34 (1986), no. 3, 489–510. MR 864452, DOI 10.1112/jlms/s2-34.3.489
- B. E. Johnson, Approximately multiplicative maps between Banach algebras, J. London Math. Soc. (2) 37 (1988), no. 2, 294–316. MR 928525, DOI 10.1112/jlms/s2-37.2.294
Bibliographic 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