Operators determining the complete norm topology of C(K)

• Autorzy: A. R. Villena
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 124
• Numer: 2
• Strony: 155-160

Daty

wydano

1997

otrzymano

1996-05-30

poprawiono

1996-12-09

Twórcy

autor

A. R. Villena

• Departamento de Analisis Matematico, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

Bibliografia

• [1] B. E. Johnson, The uniqueness of the (complete) norm topology, Bull. Amer. Math. Soc. 73 (1967), 537-539.
• [2] A. Rodríguez, The uniqueness of the complete norm topology in complete normed nonassociative algebras, J. Funct. Anal. 60 (1985), 1-15.
• [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.