#### Glasnik Matematicki, Vol. 33, No.1 (1998), 93-96.

### ON A CHARACTERIZATION OF POLYNOMIALLY BARRELED
SPACES

### 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.**
46E40.

**Key words and phrases.** Locally convex spaces, continuous
*m*-homogeneous polynomials, topology of pointwise convergence,
equicontinuous sets, closed graph theorem.

**Full text (PDF)** (free access)

*Glasnik Matematicki* Home Page