En esta nota consideramos una clase de espacios topológicos de Hausdorff localmente compactos (Ω) con la propiedad de que el espacio de Banach C0(Ω) de todas las funciones continuas con valores escalares definidas en Ω que se anulan en el infinito, equipado con la norma supremo, contiene una copia de C0 norma-uno complementada, mientras que C (βΩ) contiene una copia de l∞ linealmente isométrica.
Let [Lambda] be a barrelled perfect (in the sense of J. Dieudonné) Köthe space of measurable functions defined on an atomless finite Radon measure space. Let X be a Banach space containing a copy of c0, then the space [Lambda(X)] of [Lambda]-Bochner integrable functions contains a complemented copy of c0.
We give sufficient conditions on Banach spaces and so that their projective tensor product , their injective tensor product , or the dual contain complemented copies of .
We prove that the direct sum and the product of countably many copies of L1[0, 1] are primary locally convex spaces. We also give some related results.
The following result is proved: Let E be a complemented subspace with an r-finite-dimensional decomposition of a nuclear Köthe space λ(A). Then E has a basis.
We describe the complete interpolating sequences for the Paley-Wiener spaces Lπp (1 < p < ∞) in terms of Muckenhoupt's (Ap) condition. For p = 2, this description coincides with those given by Pavlov [9], Nikol'skii [8] and Minkin [7] of the unconditional bases of complex exponentials in L2(-π,π). While the techniques of these authors are linked to the Hilbert space geometry of Lπ2, our method of proof is based in turning the problem into one about boundedness of the Hilbert transform...
We describe the subspaces of (1 ≤ p ≠ 2 < ∞) which are the range of a completely contractive projection.