# Some algebras without submultiplicative norms or positive functionals

Studia Mathematica (1995)

- Volume: 116, Issue: 3, page 299-302
- ISSN: 0039-3223

## Access Full Article

top## Abstract

top## How to cite

topMeyer, Michael. "Some algebras without submultiplicative norms or positive functionals." Studia Mathematica 116.3 (1995): 299-302. <http://eudml.org/doc/216236>.

@article{Meyer1995,

abstract = {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.},

author = {Meyer, Michael},

journal = {Studia Mathematica},

keywords = {submultiplicative norms; positive functionals; nonexistence of submultiplicative norms; positive linear functional; submultiplicative seminorm},

language = {eng},

number = {3},

pages = {299-302},

title = {Some algebras without submultiplicative norms or positive functionals},

url = {http://eudml.org/doc/216236},

volume = {116},

year = {1995},

}

TY - JOUR

AU - Meyer, Michael

TI - Some algebras without submultiplicative norms or positive functionals

JO - Studia Mathematica

PY - 1995

VL - 116

IS - 3

SP - 299

EP - 302

AB - 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.

LA - eng

KW - submultiplicative norms; positive functionals; nonexistence of submultiplicative norms; positive linear functional; submultiplicative seminorm

UR - http://eudml.org/doc/216236

ER -

## References

top- [1] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, Berlin, 1973. Zbl0271.46039
- [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.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.