Let X be any topological space, and let C(X) be the algebra of all continuous complex-valued functions on X. We prove a conjecture of Yood (1994) to the effect that if there exists an unbounded element of C(X) then C(X) cannot be made into a normed algebra.
@article{bwmeta1.element.bwnjournal-article-smv116i3p295bwm,
author = {Alexander Pruss},
title = {A remark on non-existence of an algebra norm for the algebra of continuous functions on a topological space admitting an unbounded continuous function},
journal = {Studia Mathematica},
volume = {113},
year = {1995},
pages = {295-297},
zbl = {0844.46014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv116i3p295bwm}
}
Pruss, Alexander. A remark on non-existence of an algebra norm for the algebra of continuous functions on a topological space admitting an unbounded continuous function. Studia Mathematica, Tome 113 (1995) pp. 295-297. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv116i3p295bwm/
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