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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Vydané v:	Journal of mathematical analysis and applications Ročník 534; číslo 1; s. 128013
Hlavní autori:	Manjegani, Seyed Mahmoud, Moomkesh, Shahla, Nasr Isfahani, Rasoul
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier Inc 01.06.2024
Predmet:	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
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Popis
Shrnutí:	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