1) For a given

locally convex space E, a convex function f : E [right arrow] R U (+[infinity]} is called a proper convex function if f (x) < [infinity] for some x [member of] E.

Generalized difference sequence spaces defined by a modulus function in a

locally convex space, Soochow J.

In this paper r stands for the set of real numbers, K will denote the field of real or complex numbers (we will call them scalars), X a Hausdorff normal topological space and E a quasi-complete

locally convex space space over K with topology generated by an increasing family of semi-norms [[parallel]*[parallel].

Maddox, Statistical convergence in a

locally convex space, Math.

In particular, when Y is a (real) separated

locally convex space, the choice H = cl(K) is allowed in (c02); and Theorem 4.

It then provides generalizations of the classical result of the Orlicz-Pettis theorem to delta multiplier convergent series with values in a

locally convex space.

Altin, Generalized difference sequence spaces defined by Orlicz function in a

locally convex space, J.

If a

locally convex space X admits an operator without closed invariant subspaces then L(X) is strongly generated by two elements.

More exactly, if in an F-space the Hahn-Banach theorem holds, then that space is necessarily

locally convex space (see e.

We then intend to use the theory of mixed topologies to give some general properties of the

locally convex space (M(X), [beta](X)).

We say that a

locally convex space (E, [tau]) is Mackey complete (M-complete) if its bounded structure Bt admits a fundamental system B of Banach discs ("completent" discs) that is, for every B in B, the vector space generated by B is a Banach space when endowed with the gauge [parallel]*[[parallel].

This paper deals with the two following general problems: (i) for any

locally convex space E, characterize in terms of E the existence of a non-empty set [SIGMA] in [N.