# Operators determining the complete norm topology of C(K)

Studia Mathematica (1997)

- Volume: 124, Issue: 2, page 155-160
- ISSN: 0039-3223

## Access Full Article

top## Abstract

top## How to cite

topVillena, A.. "Operators determining the complete norm topology of C(K)." Studia Mathematica 124.2 (1997): 155-160. <http://eudml.org/doc/216404>.

@article{Villena1997,

abstract = {For any uniformly closed subalgebra A of C(K) for a compact Hausdorff space K without isolated points and $x_\{0\} ∈ A$, we show that every complete norm on A which makes continuous the multiplication by $x_\{0\}$ is equivalent to $∥·∥_\{∞\}$ provided that $x_\{0\}^\{-1\}(λ)$ has no interior points whenever λ lies in ℂ. Actually, these assertions are equivalent if A = C(K).},

author = {Villena, A.},

journal = {Studia Mathematica},

keywords = {uniformly closed subalgebra; complete norm},

language = {eng},

number = {2},

pages = {155-160},

title = {Operators determining the complete norm topology of C(K)},

url = {http://eudml.org/doc/216404},

volume = {124},

year = {1997},

}

TY - JOUR

AU - Villena, A.

TI - Operators determining the complete norm topology of C(K)

JO - Studia Mathematica

PY - 1997

VL - 124

IS - 2

SP - 155

EP - 160

AB - For any uniformly closed subalgebra A of C(K) for a compact Hausdorff space K without isolated points and $x_{0} ∈ A$, we show that every complete norm on A which makes continuous the multiplication by $x_{0}$ is equivalent to $∥·∥_{∞}$ provided that $x_{0}^{-1}(λ)$ has no interior points whenever λ lies in ℂ. Actually, these assertions are equivalent if A = C(K).

LA - eng

KW - uniformly closed subalgebra; complete norm

UR - http://eudml.org/doc/216404

ER -

## References

top- [1] B. E. Johnson, The uniqueness of the (complete) norm topology, Bull. Amer. Math. Soc. 73 (1967), 537-539. Zbl0172.41004
- [2] A. Rodríguez, The uniqueness of the complete norm topology in complete normed nonassociative algebras, J. Funct. Anal. 60 (1985), 1-15. Zbl0602.46055
- [3] Z. Semadeni, Banach Spaces of Continuous Functions, I, Polish Sci. Publ., 1971.
- [4] A. M. Sinclair, Automatic Continuity of Linear Operators, Cambridge University Press, 1976. Zbl0313.47029

## NotesEmbed ?

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