Some algebras without submultiplicative norms or positive functionals
Studia Mathematica (1995)
- Volume: 116, Issue: 3, page 299-302
- ISSN: 0039-3223
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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.
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