We prove a conjecture of Yood regarding the nonexistence of submultiplicative norms on the algebra C(T) of all continuous functions on a topological space T which admits an unbounded continuous function. We also exhibit a quotient of C(T) which does not admit a nonzero positive linear functional. Finally, it is shown that the algebra L(X) of all linear operators on an infinite-dimensional vector space X admits no nonzero submultiplicative seminorm.
@article{bwmeta1.element.bwnjournal-article-smv116i3p299bwm,
author = {Michael Meyer},
title = {Some algebras without submultiplicative norms or positive functionals},
journal = {Studia Mathematica},
volume = {113},
year = {1995},
pages = {299-302},
zbl = {0838.46041},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv116i3p299bwm}
}
Meyer, Michael. Some algebras without submultiplicative norms or positive functionals. Studia Mathematica, Tome 113 (1995) pp. 299-302. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv116i3p299bwm/
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[00002] [3] B. Yood, On the nonexistence of norms for some algebras of functions, Studia Math. 111 (1994), 97-101.