A -algebra without generalized topological divisors of zero
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Hugo Peimbert, Wiesław Żelazko (1985)
Studia Mathematica
Antonio Moreno Galindo, Ángel Rodríguez Palacios (2005)
Studia Mathematica
We prove that, for a compact metric space X not reduced to a point, the existence of a bilinear mapping ⋄: C(X) × C(X) → C(X) satisfying ||f⋄g|| = ||f|| ||g|| for all f,g ∈ C(X) is equivalent to the uncountability of X. This is derived from a bilinear version of Holsztyński's theorem [3] on isometries of C(X)-spaces, which is also proved in the paper.
Chaisuriya, Pachara (2011)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
Karakhanyan, M.I., Khor'kova, T.A. (2009)
Sibirskij Matematicheskij Zhurnal
W. Żelazko (2005)
Banach Center Publications
In this paper we extend the characterization of characters given in [1], [2] and [8] onto m-pseudoconvex algebras. As a consequence (and a generalization) we give a characterization of continuous homomorphisms from m-pseudoconvex algebras into commutative semisimple m-pseudoconvex algebras.
M. Benslimane, L. Mesmoudi, A. Rodríguez Palacios (2000)
Extracta Mathematicae
W. Żelazko (2005)
Studia Mathematica
We prove that a real or complex F-algebra has all left and right ideals closed if and only if it is noetherian.
George Maltese, Regina Wille-Fier (1988)
Studia Mathematica
Maria Fragoulopoulou (1992)
Studia Mathematica
A question of Warner and Whitley concerning a nonunital version of the Gleason-Kahane-Żelazko theorem is considered in the context of nonnormed topological algebras. Among other things it is shown that a closed hyperplane M of a commutative symmetric F*-algebra E with Lindelöf Gel'fand space is a maximal regular ideal iff each element of M belongs to some closed maximal regular ideal of E.
S. Kowalski, Z. Słodkowski (1980)
Studia Mathematica
W. Żelazko (2004)
Studia Mathematica
We prove that a real or complex unital F-algebra is a Q-algebra if and only if all its maximal one-sided ideals are closed.
Franekic, Damir (1982)
International Journal of Mathematics and Mathematical Sciences
Huzihiro Araki (1980)
Recherche Coopérative sur Programme n°25
Donald Z. Spicer (1973)
Colloquium Mathematicae
David P. Blecher (1995)
Mathematische Annalen
Vladimír Kordula, Vladimír Müller (1996)
Czechoslovak Mathematical Journal
Michael Leinert (1973)
Manuscripta mathematica
Zbigniew Słodkowski (1982)
Studia Mathematica
Alonso Takahashi (1979)
Revista colombiana de matematicas
Kim, Sung Guen (1993)
International Journal of Mathematics and Mathematical Sciences
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