On Q, QM and QM#-algebras

• Autorzy: Arizmendi-Peimbert H. , Carrillo-Hoyo A. , Valov V.
• Języki publikacji: EN

Abstrakty

EN

The concepts of Q_M and Q_M#-algebras were defined in [4] as generalizations of Q-algebras. In this paper we prove that, if X is a completely regular Hausdorff space, then the uniform topology σ is the only topology τ on C_b (X) which is coarser than σ and possesses the following property: A = (C_b (X), τ) is a topological algebra and the above three concepts are equivalent for A. We also construct a B₀-algebra which is a Q_M-algebra, but it is not a Q-algebra.

Słowa kluczowe

EN

topological algebra; Q-algebra; B0-algebra

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2002
• Tom: [Z] 42(2)
• Strony: 137--143
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Arizmendi-Peimbert H.

• Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, 04510 México, D. F.

autor

Carrillo-Hoyo A.

• Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, 04510 México, D. F.

autor

Valov V.

• Department of Computer Science and Mathematics, Nipissing University, 100 College Drive, P.O. Box 5002, North Bay, ON, P1B 8L7, Canada

Bibliografia

• [1] Arizmendi, H. On the spectral radius of a matrix algebra, Funct. Approx. Comment. Math. 19 (1990), 167-176.
• [2] Arizmendi, H. and Carrillo, A. On locally convex algebras with cyclic bases, Function spaces, The second conference. Marcel Decker. Lecture Notes in Pure and Appl. Math. 172 (1995), 11-17.
• [3] Arizmendi, H. and Jarosz, K. Extended spectral radius in topological algebras, Rocky Mount. Jour. Math. (1993), 1179-1195.
• [4] Arizmendi, H. and Valov, V. Some characterizations of Q-algebras, Comment. Math. Prace Mat. 39 (1999), 11-21.
• [5] Buck, R. C. Bounded continuous functions on a locally compact space, Michigan Math. J. 5 (1958), 95-104.
• [6] Żelazko, W. A non-m-convex algebra on which operates all entire functions, Ann. Pol. Math. 46 (1985), 389-394.