| Title:
|
A remark on supra-additive and supra-multiplicative operators on $C(X)$ (English) |
| Author:
|
Ercan, Z. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
132 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
55-58 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
M. Radulescu proved the following result: Let $X$ be a compact Hausdorff topological space and ${\pi }\: C(X)\rightarrow C(X)$ a supra-additive and supra-multiplicative operator. Then ${\pi }$ is linear and multiplicative. We generalize this result to arbitrary topological spaces. (English) |
| Keyword:
|
$C(X)$-space |
| Keyword:
|
supra-additive |
| Keyword:
|
supra-multiplicative operator |
| Keyword:
|
realcompact space |
| Keyword:
|
realcompact |
| MSC:
|
46E25 |
| MSC:
|
46E35 |
| MSC:
|
46J10 |
| MSC:
|
47B38 |
| MSC:
|
54C35 |
| idZBL:
|
Zbl 1174.46326 |
| idMR:
|
MR2311753 |
| DOI:
|
10.21136/MB.2007.133995 |
| . |
| Date available:
|
2009-09-24T22:29:06Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133995 |
| . |
| Reference:
|
[1] C. D. Aliprantis, O. Burkinshaw: Positive Operators.Academic Press, New York, 1985. MR 0809372 |
| Reference:
|
[2] Z. Ercan, S. Önal: A remark on the homomorphism on $C(X)$.Proc. Amer. Math. Soc. 133 (2005), 3609–3611. MR 2163596, 10.1090/S0002-9939-05-07930-X |
| Reference:
|
[3] K. P. Hart, J. Nagata, J. E. Vaughan: Encyclopedia of General Topology.Elsevier, Amsterdam, 2004. MR 2049453 |
| Reference:
|
[4] M. Radulescu: On a supra-additive and supra-multiplicative operator of $C(X)$.Bull. Math. Soc. Sci. Math. Répub. Soc. Roum., Nouv. Sér. 24 (1980), 303–305. Zbl 0463.47034, MR 0611909 |
| . |
