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The uniform separation property and Banach-Stone theorems for lattice-valued Lipschitz functions
Author(s):
A.
Jiménez-Vargas;
A.
Morales
Campoy;
Moisés
Villegas-Vallecillos
Journal:
Proc. Amer. Math. Soc.
137
(2009),
3769-3777.
MSC (2000):
Primary 46E40, 46E05
Posted:
June 1, 2009
Errata:
Proc. Amer. Math. Soc. 138 (2010), 1535
MathSciNet review:
2529886
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Additional information
Abstract:
Using the uniform separation property of N. Weaver and the uniform joint property, we present in this paper a Lipschitz version of a Banach-Stone-type theorem for lattice-valued continuous functions obtained recently by J. X. Chen, Z. L. Chen and N.-C. Wong.
References:
-
- 1.
- C. D. Aliprantis and O. Burkinshaw, Positive Operators, Pure and Applied Mathematics, vol. 119, Academic Press, New York, 1985. MR 809372 (87h:47086)
- 2.
- F. Cabello Sánchez, J. Cabello Sánchez, Z. Ercan and S. Önal, Memorandum on multiplicative bijections and order, available at http://kolmogorov.unex.es/~fcabello.
- 3.
- F. Cabello Sánchez and J. Cabello Sánchez, Nonlinear isomorphisms of lattices of Lipschitz functions, available at http://kolmogorov.unex.es/~fcabello.
- 4.
- J. Cao, I. Reilly and H. Xiong, A lattice-valued Banach-Stone theorem, Acta Math. Hungar. 98 (2003), 103-110. MR 1958470 (2003m:46028)
- 5.
- J. X. Chen, Z. L. Chen and N.-G. Wong, A Banach-Stone theorem for Riesz isomorphisms of Banach lattices, Proc. Amer. Math. Soc. 136 (2008), 3869-3874. MR 2425726
- 6.
- Z. Ercan and S. Önal, Banach-Stone theorem for Banach lattice valued continuous functions, Proc. Amer. Math. Soc. 135 (2007), 2827-2829. MR 2317958 (2008a:46038)
- 7.
- Z. Ercan and S. Önal, The Banach-Stone theorem revisited, Topology Appl. 155 (2008), 1800-1803. MR 2445303
- 8.
- M. I. Garrido and J. A. Jaramillo, Homomorphisms on function lattices, Monatsh. Math. 141 (2004), 127-146. MR 2037989 (2004k:46034)
- 9.
- M. I. Garrido and J. A. Jaramillo, Lipschitz-type functions on metric spaces, J. Math. Anal. Appl. 340 (2008), 282-290. MR 2376153 (2008m:46063)
- 10.
- G. J. O. Jameson, Ordered Linear Spaces, Lecture Notes in Math., vol. 141, Springer-Verlag, Berlin, 1970. MR 0438077 (55:10996)
- 11.
- A. Jiménez-Vargas and Moisés Villegas-Vallecillos, Order isomorphisms of little Lipschitz algebras, Houston J. Math. 34 (2008), 1185-1195. MR 2465374
- 12.
- X. Miao, J. Cao and H. Xiong, Banach-Stone theorems and Riesz algebras, J. Math. Anal. Appl. 313 (2006), 177-183. MR 2178729 (2006m:46030)
- 13.
- N. Weaver, Lattices of Lipschitz functions, Pacific. J. Math. 164 (1994), 179-193. MR 1267506 (95b:46031)
- 14.
- N. Weaver, Order completeness in Lipschitz algebras, J. Funct. Anal. 130 (1995), 118-130. MR 1331979 (96f:46048)
- 15.
- N. Weaver, Subalgebras of little Lipschitz algebras, Pacific. J. Math. 173 (1996), 283-293. MR 1387803 (97f:46083)
- 16.
- N. Weaver, Quotients of little Lipschitz algebras, Proc. Amer. Math. 125 (1997), 2643-2648. MR 1402889 (97j:46021)
- 17.
- N. Weaver, Lipschitz algebras, World Scientific Publishing Co., River Edge, NJ, 1999. MR 1832645 (2002g:46002)
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Additional Information:
A.
Jiménez-Vargas
Affiliation:
Departamento de Álgebra y Análisis Matemático, Universidad de Almería, 04120 Almería, Spain
Email:
ajimenez@ual.es
A.
Morales
Campoy
Affiliation:
Departamento de Álgebra y Análisis Matemático, Universidad de Almería, 04120 Almería, Spain
Email:
amorales@ual.es
Moisés
Villegas-Vallecillos
Affiliation:
Departamento de Álgebra y Análisis Matemático, Universidad de Almería, 04120 Almería, Spain
Email:
mvv042@alboran.ual.es
DOI:
10.1090/S0002-9939-09-09941-9
PII:
S 0002-9939(09)09941-9
Keywords:
Vector lattice isomorphism,
lattice-valued Lipschitz function,
Banach--Stone theorem,
uniform separation property
Received by editor(s):
February 12, 2009,
Received by editor(s) in revised form:
February 20, 2009
Posted:
June 1, 2009
Additional Notes:
This research was partially supported by Junta de Andalucía grants FQM-1438 and FQM-3737, and MCYT projects MTM2006-4837 and MTM2007-65959.
The third author was supported in part by Beca Plan Propio Universidad de Almería
Communicated by:
Nigel J. Kalton
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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