Alexander Pruss (1995)
Studia Mathematica
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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.
Bohdan Tomiuk, Bertram Yood (1989)
Studia Mathematica
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Wiesław Żelazko (1963)
Colloquium Mathematicae
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Bertram Yood (1994)
Studia Mathematica
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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 where ℝ is the reals.
ÁNGEL RODRÍGUEZ PALACIOS (2000)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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A. Beddaa, M. Oudadess (1989)
Studia Mathematica
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Emeric Deutsch (1973)
Studia Mathematica
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A. Iwanik (1996)
Studia Mathematica
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We construct strictly ergodic 0-1 Toeplitz flows with pure point spectrum and irrational eigenvalues. It is also shown that the property of being regular is not a measure-theoretic invariant for strictly ergodic Toeplitz flows.
María D. Acosta (1995)
Extracta Mathematicae
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C. J. Read (2005)
Studia Mathematica
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It is a long standing open problem whether there is any infinite-dimensional commutative Banach algebra without nontrivial closed ideals. This is in some sense the Banach algebraists' counterpart to the invariant subspace problem for Banach spaces. We do not here solve this famous problem, but solve a related problem, that of finding (necessarily commutative) infinite-dimensional normed algebras which do not even have nontrivial closed subalgebras. Our examples are incomplete normed...
E. Strzelecki (1963)
Studia Mathematica
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