A remark on supra-additive and supra-multiplicative operators on C ( X )

Zafer Ercan

Mathematica Bohemica (2007)

  • Volume: 132, Issue: 1, page 55-58
  • ISSN: 0862-7959

Abstract

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M. Radulescu proved the following result: Let X be a compact Hausdorff topological space and π C ( X ) → C ( X ) a supra-additive and supra-multiplicative operator. Then π is linear and multiplicative. We generalize this result to arbitrary topological spaces.

How to cite

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Ercan, Zafer. "A remark on supra-additive and supra-multiplicative operators on $C(X)$." Mathematica Bohemica 132.1 (2007): 55-58. <http://eudml.org/doc/250243>.

@article{Ercan2007,
abstract = {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.},
author = {Ercan, Zafer},
journal = {Mathematica Bohemica},
keywords = {$C(X)$-space; supra-additive; supra-multiplicative operator; realcompact space; realcompact; -space; realcompact space},
language = {eng},
number = {1},
pages = {55-58},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A remark on supra-additive and supra-multiplicative operators on $C(X)$},
url = {http://eudml.org/doc/250243},
volume = {132},
year = {2007},
}

TY - JOUR
AU - Ercan, Zafer
TI - A remark on supra-additive and supra-multiplicative operators on $C(X)$
JO - Mathematica Bohemica
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 132
IS - 1
SP - 55
EP - 58
AB - 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.
LA - eng
KW - $C(X)$-space; supra-additive; supra-multiplicative operator; realcompact space; realcompact; -space; realcompact space
UR - http://eudml.org/doc/250243
ER -

References

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  1. Positive Operators, Academic Press, New York, 1985. (1985) MR0809372
  2. 10.1090/S0002-9939-05-07930-X, Proc. Amer. Math. Soc. 133 (2005), 3609–3611. (2005) MR2163596DOI10.1090/S0002-9939-05-07930-X
  3. Encyclopedia of General Topology, Elsevier, Amsterdam, 2004. (2004) MR2049453
  4. 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. (1980) Zbl0463.47034MR0611909

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