Operators determining the complete norm topology of C(K)
Villena, A.
Studia Mathematica, Tome 122 (1997), p. 155-160 / Harvested from The Polish Digital Mathematics Library
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For any uniformly closed subalgebra A of C(K) for a compact Hausdorff space K without isolated points and x0∈A, we show that every complete norm on A which makes continuous the multiplication by x0 is equivalent to ∥·∥∞ provided that x0-1(λ) has no interior points whenever λ lies in ℂ. Actually, these assertions are equivalent if A = C(K).

Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:216404 
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Villena, A. Operators determining the complete norm topology of C(K). Studia Mathematica, Tome 122 (1997) pp. 155-160. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv124i2p155bwm/

[00000] [1] B. E. Johnson, The uniqueness of the (complete) norm topology, Bull. Amer. Math. Soc. 73 (1967), 537-539. | Zbl 0172.41004

[00001] [2] A. Rodríguez, The uniqueness of the complete norm topology in complete normed nonassociative algebras, J. Funct. Anal. 60 (1985), 1-15. | Zbl 0602.46055

[00002] [3] Z. Semadeni, Banach Spaces of Continuous Functions, I, Polish Sci. Publ., 1971.

[00003] [4] A. M. Sinclair, Automatic Continuity of Linear Operators, Cambridge University Press, 1976. | Zbl 0313.47029