Several properties of the class of minimal Orlicz function spaces LF are described. In particular, an explicitly defined class of non-trivial minimal functions is shown, which provides concrete examples of Orlicz spaces without complemented copies of F-spaces.
We study the mappings of monotone type in Orlicz-Sobolev spaces. We introduce a new class as a generalization of and extend the definition of quasimonotone map. We also prove existence results for equations involving monotone-like mappings.
The space of multilinear mappings of nuclear type (s;r1,...,rn) between Banach spaces is considered, some of its properties are described (including the relationship with tensor products) and its topological dual is characterized as a Banach space of absolutely summing mappings.
We introduce and examine the notion of dense weak openness. In particular we show that multiplication in C(X) is densely weakly open whenever X is an interval in ℝ.
It is proved that a Musielak-Orlicz space LΦ of real valued functions which is isometric to a Hilbert space coincides with L2 up to a weight, that is Φ(u,t) = c(t) u2. Moreover it is shown that any surjective isometry between LΦ and L∞ is a weighted composition operator and a criterion for LΦ to be isometric to L∞ is presented.
Let E be a Fréchet Schwartz space with a continuous norm and with a finite-dimensional decomposition, and let F be any infinite-dimensional subspace of E. It is proved that E can be written as G ⨁ H where G and H do not contain any subspace isomorphic to F. In particular, E is not primary. If the subspace F is not normable then the statement holds for other quasinormable Fréchet spaces, e.g., if E is a quasinormable and locally normable Köthe sequence space, or if E is a space of holomorphic functions...
Si K es un compacto no vacío en Rr, damos una condición suficiente para que la inyección canónica de ε{M},b(K) en ε{M},d(K) sea nuclear. Consideramos el caso mixto y obtenemos la existencia de un operador de extensión nuclear de ε{M1}(F)A en ε{M2}(Rr)D donde F es un subconjunto cerrado propio de Rr y A y D son discos de Banach adecuados. Finalmente aplicamos este último resultado al caso Borel, es decir cuando F = {0}.