# A remark on non-existence of an algebra norm for the algebra of continuous functions on a topological space admitting an unbounded continuous function

Studia Mathematica (1995)

- Volume: 116, Issue: 3, page 295-297
- ISSN: 0039-3223

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topPruss, Alexander. "A remark on non-existence of an algebra norm for the algebra of continuous functions on a topological space admitting an unbounded continuous function." Studia Mathematica 116.3 (1995): 295-297. <http://eudml.org/doc/216235>.

@article{Pruss1995,

abstract = {Let X be any topological space, and let C(X) be the algebra of all continuous complex-valued functions on X. We prove a conjecture of Yood (1994) to the effect that if there exists an unbounded element of C(X) then C(X) cannot be made into a normed algebra.},

author = {Pruss, Alexander},

journal = {Studia Mathematica},

keywords = {algebra of all continuous functions; normed commutative algebra; non-existence of norm; topological spaces admitting unbounded functions; algebra of all continuous complex-valued functions; unbounded element},

language = {eng},

number = {3},

pages = {295-297},

title = {A remark on non-existence of an algebra norm for the algebra of continuous functions on a topological space admitting an unbounded continuous function},

url = {http://eudml.org/doc/216235},

volume = {116},

year = {1995},

}

TY - JOUR

AU - Pruss, Alexander

TI - A remark on non-existence of an algebra norm for the algebra of continuous functions on a topological space admitting an unbounded continuous function

JO - Studia Mathematica

PY - 1995

VL - 116

IS - 3

SP - 295

EP - 297

AB - Let X be any topological space, and let C(X) be the algebra of all continuous complex-valued functions on X. We prove a conjecture of Yood (1994) to the effect that if there exists an unbounded element of C(X) then C(X) cannot be made into a normed algebra.

LA - eng

KW - algebra of all continuous functions; normed commutative algebra; non-existence of norm; topological spaces admitting unbounded functions; algebra of all continuous complex-valued functions; unbounded element

UR - http://eudml.org/doc/216235

ER -

## References

top- [1] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, 1973. Zbl0271.46039
- [2] I. Kaplansky, Normed algebras, Duke Math. J. 16 (1949), 399-418. Zbl0033.18701
- [3] T. W. Palmer, Banach Algebras and the General Theory of *-Algebras. Volume I: Algebras and Banach Algebras, Encyclopedia Math. Appl. 49, Cambridge Univ. Press, 1994. Zbl0809.46052
- [4] B. Yood, On the nonexistence of norms for some algebras of functions, Studia Math. 111 (1994), 97-101.

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