Continuity of homomorphisms into normed algebras without topological divisors of zero.
ÁNGEL RODRÍGUEZ PALACIOS (2000)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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Displaying similar documents to “On topological divisors of zero in p-normed algebras without unit”
Continuity of homomorphisms into normed algebras without topological divisors of zero.
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A remark on non-existence of an algebra norm for the algebra of continuous functions on a topological space admitting an unbounded continuous function
Alexander Pruss (1995)
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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.
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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.
Topological Properties of Real Normed Space
Kazuhisa Nakasho, Yuichi Futa, Yasunari Shidama (2014)
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In this article, we formalize topological properties of real normed spaces. In the first part, open and closed, density, separability and sequence and its convergence are discussed. Then we argue properties of real normed subspace. Then we discuss linear functions between real normed speces. Several kinds of subspaces induced by linear functions such as kernel, image and inverse image are considered here. The fact that Lipschitz continuity operators preserve convergence of sequences...
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Miguel Cabrera García, Angel Rodríguez Palacios (1990)
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Recently M. Mathieu [9] has proved that any associative ultraprime normed complex algebra is centrally closed. The aim of this note is to announce the general nonassociative extension of Mathieu's result obtained by the authors [2].
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E.R. Lorch (1952)
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