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}.
In this paper there is proved that every Musielak-Orlicz space is reflexive iff it is -convex. This is an essential extension of the results given by Ye Yining, He Miaohong and Ryszard Płuciennik [16].
Pointwise interpolation inequalities, in particular, ku(x)c(Mu(x)) 1-k/m (Mmu(x))k/m, k<m, and |Izf(x)|c (MIf(x))Re z/Re (Mf(x))1-Re z/Re , 0<Re z<Re<n, where is the gradient of order , is the Hardy-Littlewood maximal operator, and is the Riesz potential of order , are proved. Applications to the theory of multipliers in pairs of Sobolev spaces are given. In particular, the maximal algebra in the multiplier space is described.