Atlas: The $m$-topology on algebras between $C^*(X)$ and $C(X)$ by J. Gomez-Perez

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Functional Analysis Valencia 2000
July 3-7, 2000
Technical University of Valencia (UPV) and University of Valencia (UV)
Valencia, Spain

Organizers
R.M. Aron (Kent State U., USA), K.D. Bierstedt (U. Paderborn, Germany), J. Bonet (UPV), J. Cerdà (U. Barcelona, Spain), H. Jarchow (U. Zürich, Switzerland), M. Maestre (UV), J. Schmets (U. Liège, Belgium)

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The m-topology on algebras between C^*(X) and C(X)
by
J. Gómez-Pérez
Departamento de Matemáticas, Universidad de León, 24071 León, Spain

Let C(X) be the algebra of all real-valued continuous functions on a completely regular space X, and C^*(X) the subalgebra of bounded functions. Any intermediate algebra A between C^*(X) and C(X) is endowed with the m_A-topology, defined in a similar way to the m-topology on C(X). The relative topology that A inherits as a subspace of C(X) is finer than the m_A-topology and, with the latter one, A is always a topological ring, but not a topological algebra. The topological properties of A are studied, and the intermediate algebras that are normed topological rings are characterized.

(T)

Date received: April 6, 2000