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

• Autorzy: Alexander R. Pruss
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 46J10: Banach algebras of continuous functions, function algebras
• 46E25: Rings and algebras of continuous, differentiable or analytic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1995
• Tom: 116
• Numer: 3
• Strony: 295-297

Daty

wydano

1995

otrzymano

1995-02-16

poprawiono

1995-06-16

Twórcy

autor

Alexander R. Pruss

• Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada V6T 1Z2

Bibliografia

• [1] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, 1973.
• [2] I. Kaplansky, Normed algebras, Duke Math. J. 16 (1949), 399-418.
• [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.
• [4] B. Yood, On the nonexistence of norms for some algebras of functions, Studia Math. 111 (1994), 97-101.