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

@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 -