On Frechet dierentiability of convex functions on Banach spaces

The invariant subspace problem for some operators and some operator alge- bras acting on a locally convex space is studied.. Keywords: invariant subspace, locally convex space,

Notions of a boundedly convex function and of a Lipschitz-continuous function are extended to the case of functions on pseudo-topological vector spaces.. It is proved that for

We show the existence of at least one Lipschitz solution for ex- tensions of convex sweeping processes in reflexive smooth Banach spaces.. Our result is proved under a weaker

Applying Theorem 2.3, Lemmas 2.7 and 2.8, we have that if D is a nonempty bounded closed convex subset of a uniformly convex and 2-uniformly smooth Banach space E, D is a

convergence in the sense of Lorentz for vector-valued bounded functions defined on a commutative semigroup with values in a locally convex space to transformation semigroups,

logical vector space with a partial ordering defined by a solid pointed

Corollary 2.2 Let $E$ be a reflexive Banach space with a uniformly Gateaux differentiable norm,. $C$ a nonempty closed convex subset of $E$ which has normal structure, and

Theorem 3.3 Let $E$ be a unifo $7^{\cdot}mly$ convex Banach $space\prime w\prime itll$ a $F_{\mathfrak{l}}\cdot\acute{e}chetdiffe\uparrow\cdot ent\prime iabl,e$ $no\uparrow\cdot