Non unicité des topologies localement-convexes complètes sur certaines algèbres

• Autorzy: Abdelali Z. , Chidami M.
• Języki publikacji: EN

Abstrakty

EN

We are interested, here, by the problems 1, 8 and 9 due to Wojciechowski and Żelazko (1997). We show that every algebra A generated by ℵ elements, such that ℵ > ℵ₀, can be a locally-convex (resp. complete locally p-convex, p ϵ (0, 1]) semitopological algebra in ℵ +1 (resp. max{2^ℵ₀, ℵ +1}) different ways, which reduce the problem 9. Moreover if ℵ^ℵ₀ = ℵ, A can be a complete locally-convex semitopological algebra in ℵ +1 different ways, which solves the problem 1 for every ℵ^ℵ₀-generated algebra. On the other hand, we prove that for every algebra of polynomials generated by ℵ indeterminates, ℵ ≥ ℵ₀ we can assign max{2^ℵ₀, ℵ +1} distinct topologies which make it a locally-convex topological algebra. Then, we get a reduction of problem 8.

Słowa kluczowe

EN

locally-convex algebra; semitopological algebra

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2002
• Tom: [Z] 42(2)
• Strony: 125--136
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Abdelali Z.

• Département de Mathématiques et Informatique, Faculté des Sciences, Université Mohammed V, B.P 1014 Rabat, Maroc

autor

Chidami M.

• Département de Mathématiques et Informatique, Faculté des Sciences, Université Mohammed V, B.P 1014 Rabat, Maroc

Bibliografia

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• [5] H. H. Schaefer, Topological Vector Speces, Springer, New York, 1971.
• [6] L. Waelbroeck, Topological Vector Speces and Algebras, Lecture Notes in Math. 230, Springer, 1991.
• [7] M. Wojciechowski and W. Żelazko, Non-uniqueness of topology for algebras of polynomials, Colloq. Math. 71 (1997), 111-121.
• [8] W. Żelazko, On certain open problems in topological algebras, Rend. Sem. Mat. Fis. Milano 59 (1989), 49-58.
• [9] W. Żelazko, On topologization of countably generated algebras, Studia Math. 112 (1994), 83-88.
• [10] W. Żelazko, Concerning topologization of P(t), Acta Univ. Lodz. Folia Math. 8 (1996), 153-159.
• [11] W. Żelazko, Concerning topologization of algebras - the results and open problems, in: Advances in Functional Analysis, New Age Internat. Publ., 1996.
• [12] W. Żelazko, A non-locally convex topological algebra with all commutative subalgebras locally convex, Studia. Math. 120 (1996).
• [13] W. Żelazko, A non-Banach m-convex algebra all of whose closed commutative subalgebras are Banach algebra, Studia. Math. 119 (1996).