Geodesic
Some algebras without submultiplicative norms or positive functionals
Studia Mathematica, Tome 116 (1995) no. 3, pp. 299-302

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm-116-3-299-302
Keywords: submultiplicative norms, positive functionals

Michael J. Meyer 1

1 
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Michael J. Meyer. Some algebras without submultiplicative norms or positive functionals. Studia Mathematica, Tome 116 (1995) no. 3, pp. 299-302. doi: 10.4064/sm-116-3-299-302

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