# On the non-existence of norms for some algebras of functions

Studia Mathematica (1994)

- Volume: 111, Issue: 1, page 97-101
- ISSN: 0039-3223

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topYood, Bertram. "On the non-existence of norms for some algebras of functions." Studia Mathematica 111.1 (1994): 97-101. <http://eudml.org/doc/216122>.

@article{Yood1994,

abstract = {Let C(Ω) be the algebra of all complex-valued continuous functions on a topological space Ω where C(Ω) contains unbounded functions. First it is shown that C(Ω) cannot have a Banach algebra norm. Then it is shown that, for certain Ω, C(Ω) cannot possess an (incomplete) normed algebra norm. In particular, this is so for $Ω = ℝ^n$ where ℝ is the reals.},

author = {Yood, Bertram},

journal = {Studia Mathematica},

keywords = {non-existence of norms; algebra of all complex-valued continuous functions on a topological space; unbounded functions},

language = {eng},

number = {1},

pages = {97-101},

title = {On the non-existence of norms for some algebras of functions},

url = {http://eudml.org/doc/216122},

volume = {111},

year = {1994},

}

TY - JOUR

AU - Yood, Bertram

TI - On the non-existence of norms for some algebras of functions

JO - Studia Mathematica

PY - 1994

VL - 111

IS - 1

SP - 97

EP - 101

AB - Let C(Ω) be the algebra of all complex-valued continuous functions on a topological space Ω where C(Ω) contains unbounded functions. First it is shown that C(Ω) cannot have a Banach algebra norm. Then it is shown that, for certain Ω, C(Ω) cannot possess an (incomplete) normed algebra norm. In particular, this is so for $Ω = ℝ^n$ where ℝ is the reals.

LA - eng

KW - non-existence of norms; algebra of all complex-valued continuous functions on a topological space; unbounded functions

UR - http://eudml.org/doc/216122

ER -

## References

top- [1] W. G. Bade and P. C. Curtis Jr., Homomorphisms of commutative Banach algebras, Amer. J. Math. 82 (1960), 589-608. Zbl0093.12503
- [2] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, 1973. Zbl0271.46039
- [3] L. Gillman and M. Jerison, Rings of Continuous Functions, Van Nostrand, Princeton, 1960. Zbl0093.30001
- [4] E. Hewitt and K. Stromberg, Real and Abstract Analysis, Springer, New York, 1965.
- [5] I. Kaplansky, Normed algebras, Duke Math. J. 16 (1949), 399-418. Zbl0033.18701
- [6] C. E. Rickart, General Theory of Banach Algebras, Van Nostrand, Princeton, 1960. Zbl0095.09702

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