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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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 534; no. 1; p. 128013
Main Authors: Manjegani, Seyed Mahmoud, Moomkesh, Shahla, Nasr Isfahani, Rasoul
Format: Journal Article
Language:English
Published: Elsevier Inc 01.06.2024
Subjects:
Fredholm operator
Locally compact space
Separating linear map
The continuous function space
Weighted composition operator
The continuous function space
Weighted composition operator
Fredholm operator
Separating linear map
Locally compact space
ISSN:0022-247X, 1096-0813
Online Access:Get full text
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Summary: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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2023.128013