Some algebras without submultiplicative norms or positive functionals

• Autorzy: Michael J. Meyer
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

submultiplicative norms; positive functionals

Kategorie tematyczne

• 46H05: General theory of topological algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1995
• Tom: 116
• Numer: 3
• Strony: 299-302

Daty

wydano

1995-07-04

otrzymano

1995-04-27

Twórcy

autor

Michael J. Meyer

• Department of Mathematics and Computer Science, Georgia State University, Atlanta, Georgia, 30303, U.S.A.

Bibliografia

• [1] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, Berlin, 1973.
• [2] S. Willard, General Topology, Addison-Wesley, Reading, 1970.
• [3] B. Yood, On the nonexistence of norms for some algebras of functions, Studia Math. 111 (1994), 97-101.