Fredholm separating maps on continuous function spaces
For locally compact Hausdorff spaces X and Y, we initiate a study of Fredholm separating maps T from C(X) into C(Y). Our key aim is to completely recognize the structures of the kernel space and the range space of T in terms of merging points to show that X and Y are homeomorphic after removing rela...
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| Veröffentlicht in: | Journal of mathematical analysis and applications Jg. 534; H. 1; S. 128013 |
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| Abstract | For locally compact Hausdorff spaces X and Y, we initiate a study of Fredholm separating maps T from C(X) into C(Y). Our key aim is to completely recognize the structures of the kernel space and the range space of T in terms of merging points to show that X and Y are homeomorphic after removing related finite subsets; as the main result, we describe the interaction between continuity of T and closedness of its range; in particular, under certain condition, we conclude that T can be represented as a weighted composition operator. |
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| AbstractList | For locally compact Hausdorff spaces X and Y, we initiate a study of Fredholm separating maps T from C(X) into C(Y). Our key aim is to completely recognize the structures of the kernel space and the range space of T in terms of merging points to show that X and Y are homeomorphic after removing related finite subsets; as the main result, we describe the interaction between continuity of T and closedness of its range; in particular, under certain condition, we conclude that T can be represented as a weighted composition operator. |
| ArticleNumber | 128013 |
| Author | Moomkesh, Shahla Manjegani, Seyed Mahmoud Nasr Isfahani, Rasoul |
| Author_xml | – sequence: 1 givenname: Seyed Mahmoud surname: Manjegani fullname: Manjegani, Seyed Mahmoud email: manjgani@cc.iut.ac.ir – sequence: 2 givenname: Shahla surname: Moomkesh fullname: Moomkesh, Shahla email: s.moomkesh@math.iut.ac.ir – sequence: 3 givenname: Rasoul surname: Nasr Isfahani fullname: Nasr Isfahani, Rasoul email: isfahani@cc.iut.ac.ir |
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| Cites_doi | 10.1017/S1446788700001099 10.1512/iumj.1983.32.32018 10.1090/S0002-9939-1984-0733403-7 10.36045/bbms/1197908896 10.1016/j.topol.2013.02.007 10.1016/j.jmaa.2010.02.041 10.1016/j.jmaa.2006.01.067 10.1016/j.jmaa.2007.04.045 10.1007/BF01246833 10.1007/BF02568002 10.1016/j.jmaa.2017.12.061 10.1007/BF01189890 10.1007/s000130050268 10.1016/1385-7258(83)90062-8 10.4153/CMB-1990-024-2 10.1006/jmaa.1996.0296 10.24193/fpt-ro.2018.1.01 |
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| Keywords | The continuous function space Weighted composition operator Fredholm operator Separating linear map Locally compact space |
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| SubjectTerms | Fredholm operator Locally compact space Separating linear map The continuous function space Weighted composition operator |
| Title | Fredholm separating maps on continuous function spaces |
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