Glasnik Matematicki, Vol. 33, No.1 (1998), 93-96.
ON A CHARACTERIZATION OF POLYNOMIALLY BARRELED
Miguel Caldas Cueva and Dinamerico P. Pombo Jr.
Instituto de Matematica, Universidade Federal Fluminense,
Rua Sao Paolo, 24020-005, RJ-Brasil
Abstract. A locally convex space E is
polynomially barrelled if and only if, for every positive integer
m and for every Banach space F, the space of all
continuous m-homogeneous polynomials from E into
F is quasi-complete for the topology of pointwise convergence.
1991 Mathematics Subject Classification.
Key words and phrases. Locally convex spaces, continuous
m-homogeneous polynomials, topology of pointwise convergence,
equicontinuous sets, closed graph theorem.
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