A note on finite codimensional linear isometries of C(X) into C(Y)
Let (X,Y) be a pair of compact Hausdorff spaces. It is shown that a certain property of the class of continuous maps of Y onto X is equivalent to the non-existence of linear isometry of C(X) into C(Y) whose range has finite codimension >0.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1995-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S016117129500086X |
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| _version_ | 1832566237660446720 |
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| author | Sin-Ei Takahasi Takateru Okayasu |
| author_facet | Sin-Ei Takahasi Takateru Okayasu |
| author_sort | Sin-Ei Takahasi |
| collection | DOAJ |
| description | Let (X,Y) be a pair of compact Hausdorff spaces. It is shown that a certain
property of the class of continuous maps of Y onto X is equivalent to the non-existence of linear
isometry of C(X) into C(Y) whose range has finite codimension >0. |
| format | Article |
| id | doaj-art-e13f89d6a451427299ff081189d98e53 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1995-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e13f89d6a451427299ff081189d98e532025-02-03T01:04:52ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251995-01-0118467768010.1155/S016117129500086XA note on finite codimensional linear isometries of C(X) into C(Y)Sin-Ei Takahasi0Takateru Okayasu1Department of Basic Technology, Applied Mathematics and Physics, Yamagata University, Yomezawa 992, JapanDepartment of Mathematics, Faculty of Science, Yamagata University, Yamagata 990, JapanLet (X,Y) be a pair of compact Hausdorff spaces. It is shown that a certain property of the class of continuous maps of Y onto X is equivalent to the non-existence of linear isometry of C(X) into C(Y) whose range has finite codimension >0.http://dx.doi.org/10.1155/S016117129500086Xcompact Hausdorff spaceC(X)linear isometryfinite codimension. |
| spellingShingle | Sin-Ei Takahasi Takateru Okayasu A note on finite codimensional linear isometries of C(X) into C(Y) International Journal of Mathematics and Mathematical Sciences compact Hausdorff space C(X) linear isometry finite codimension. |
| title | A note on finite codimensional linear isometries of C(X) into C(Y) |
| title_full | A note on finite codimensional linear isometries of C(X) into C(Y) |
| title_fullStr | A note on finite codimensional linear isometries of C(X) into C(Y) |
| title_full_unstemmed | A note on finite codimensional linear isometries of C(X) into C(Y) |
| title_short | A note on finite codimensional linear isometries of C(X) into C(Y) |
| title_sort | note on finite codimensional linear isometries of c x into c y |
| topic | compact Hausdorff space C(X) linear isometry finite codimension. |
| url | http://dx.doi.org/10.1155/S016117129500086X |
| work_keys_str_mv | AT sineitakahasi anoteonfinitecodimensionallinearisometriesofcxintocy AT takateruokayasu anoteonfinitecodimensionallinearisometriesofcxintocy AT sineitakahasi noteonfinitecodimensionallinearisometriesofcxintocy AT takateruokayasu noteonfinitecodimensionallinearisometriesofcxintocy |