Complemented *-primitive Ideals in L1-algebras of Exponential Lie Groups and of Motion Groups.
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.
In this paper, we introduce and study the notion of completely bounded sets ( for short) for compact, non-abelian groups G. We characterize sets in terms of completely bounded multipliers. We prove that when G is an infinite product of special unitary groups of arbitrarily large dimension, there are sets consisting of representations of unbounded degree that are sets for all p < ∞, but are not for any p ≥ 4. This is done by showing that the space of completely bounded multipliers...
The purpose of this note is to announce, without proofs, some results concerning vector valued multilinear operators on a product of C(K) spaces.
A Banach space X has the Dunford-Pettis property (DPP) provided that every weakly compact operator T from X to any Banach space Y is completely continuous (or a Dunford-Pettis operator). It is known that X has the DPP if and only if every weakly null sequence in X is a Dunford-Pettis subset of X. In this paper we give equivalent characterizations of Banach spaces X such that every weakly Cauchy sequence in X is a limited subset of X. We prove that every operator T: X → c₀ is completely continuous...