- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 741050, 8 pages
Nonvanishing Preservers and Compact Weighted Composition Operators between Spaces of Lipschitz Functions
1School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
2School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China
3Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li 32023, Taiwan
Received 14 June 2013; Accepted 9 September 2013
Academic Editor: Fabio M. Camilli
Copyright © 2013 Dongyang Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- M. I. Garrido and J. A. Jaramillo, “Variations on the Banach-Stone theorem,” Extracta Mathematicae, vol. 17, no. 3, pp. 351–383, 2002.
- K. Jarosz and V. D. Pathak, “Isometries and small bound isomorphisms of function spaces,” in Function Spaces, K. Jarosz, Ed., vol. 136 of Lecture Notes in Pure and Applied Mathematics, pp. 241–271, Marcel Dekker, New York, NY, USA, 1992.
- H. Kamowitz, “Compact weighted endomorphisms of ,” Proceedings of the American Mathematical Society, vol. 83, no. 3, pp. 517–521, 1981.
- J. Cao, I. Reilly, and H. Xiong, “A lattice-valued Banach-Stone theorem,” Acta Mathematica Hungarica, vol. 98, no. 1-2, pp. 103–110, 2003.
- J.-X. Chen, Z. L. Chen, and N. Wong, “A banach-stone theorem for riesz isomorphisms of banach lattices,” Proceedings of the American Mathematical Society, vol. 136, no. 11, pp. 3869–3874, 2008.
- Z. Ercan and S. Önal, “Banach-stone theorem for Banach lattice valued continuous functions,” Proceedings of the American Mathematical Society, vol. 135, no. 9, pp. 2827–2829, 2007.
- Z. Ercan and S. Önal, “The Banach-Stone theorem revisited,” Topology and its Applications, vol. 155, no. 16, pp. 1800–1803, 2008.
- X. Miao, J. Cao, and H. Xiong, “Banach-Stone theorems and Riesz algebras,” Journal of Mathematical Analysis and Applications, vol. 313, no. 1, pp. 177–183, 2006.
- M. I. Garrido and J. A. Jaramillo, “Homomorphisms on function lattices,” Monatshefte fur Mathematik, vol. 141, no. 2, pp. 127–146, 2004.
- M. I. Garrido and J. A. Jaramillo, “Lipschitz-type functions on metric spaces,” Journal of Mathematical Analysis and Applications, vol. 340, no. 1, pp. 282–290, 2008.
- N. Weaver, “Lattices of Lipschitz functions,” Pacific Journal of Mathematics, vol. 164, pp. 179–193, 1994.
- A. Jiménez-Vargas and M. Villegas-Vallecillos, “Order isomorphisms of little Lipschitz algebras,” Houston Journal of Mathematics, vol. 34, no. 4, pp. 1185–1195, 2008.
- A. Jiménez-Vargas, A. M. Campoy, and M. Villegas-Vallecillos, “The uniform separation property and banach-stone theorems for lattice-valued lipschitz functions,” Proceedings of the American Mathematical Society, vol. 137, no. 11, pp. 3769–3777, 2009.
- L. Dubarbie, “Maps preserving common zeros between subspaces of vector-valued continuous functions,” Positivity, vol. 14, no. 4, pp. 695–703, 2010.
- J. Araujo and L. Dubarbie, “Biseparating maps between Lipschitz function spaces,” Journal of Mathematical Analysis and Applications, vol. 357, no. 1, pp. 191–200, 2009.
- L. Li and D. Leung, “Order isomorphisms on function space,” Studia Mathematica. In press.
- L. Li and N.-C. Wong, “Kaplansky theorem of completely regular spaces,” Proceedings of the American Mathematical Society. In press.
- N. Weaver, Lipschitz Algebras, World Scientific Pbulishing, Singapore, 1999.
- H. Kamowitz and S. Scheinberg, “Some properties of endomorphisms of Lipschitz algebras,” Studia Mathematica, vol. 96, no. 3, pp. 383–391, 1990.
- A. Jiménez-Vargas and M. Villegas-Vallecillos, “Compact composition operators on noncompact Lipschitz spaces,” Journal of Mathematical Analysis and Applications, vol. 398, no. 1, pp. 221–229, 2013.