On the non-existence of norms for some algebras of functions

• Autorzy: Bertram Yood
• Języki publikacji: EN

Abstrakty

EN

Let C(Ω) be the algebra of all complex-valued continuous functions on a topological space Ω where C(Ω) contains unbounded functions. First it is shown that C(Ω) cannot have a Banach algebra norm. Then it is shown that, for certain Ω, C(Ω) cannot possess an (incomplete) normed algebra norm. In particular, this is so for $Ω = ℝ^n$ where ℝ is the reals.

Kategorie tematyczne

• 46E25: Rings and algebras of continuous, differentiable or analytic functions
• 46J05: General theory of commutative topological algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1994
• Tom: 111
• Numer: 1
• Strony: 97-101

Daty

wydano

1994

otrzymano

1993-11-25

poprawiono

1994-03-07

Twórcy

autor

Bertram Yood

• Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802, U.S.A.

Bibliografia

• [1] W. G. Bade and P. C. Curtis Jr., Homomorphisms of commutative Banach algebras, Amer. J. Math. 82 (1960), 589-608.
• [2] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, 1973.
• [3] L. Gillman and M. Jerison, Rings of Continuous Functions, Van Nostrand, Princeton, 1960.
• [4] E. Hewitt and K. Stromberg, Real and Abstract Analysis, Springer, New York, 1965.
• [5] I. Kaplansky, Normed algebras, Duke Math. J. 16 (1949), 399-418.
• [6] C. E. Rickart, General Theory of Banach Algebras, Van Nostrand, Princeton, 1960.