In this note the almost sure convergence of stationary, '-mixing sequences of random variables with values in real, separable Banach spaces according to summability methods is linked to the fullllment of a certain integrability condition generalizing and extending the results for i.i.d. sequences. Furthermore we give via Baum-Katz type results an estimate for the rate of convergence in these laws.

We provide a new proof of James’ sup theorem for (non necessarily separable) Banach spaces. One of the ingredients is the following generalization of a theorem of Hagler and Johnson ([5]) : “If a normed space E does not contain any asymptotically isometric copy of l(N), then every bounded sequence of E′ has a normalized block sequence pointwise converging to 0”.

Let E be a separable Banach space and Ω be a compact Hausdorff space. It is shown that the space C(Ω, E) has property (V) if and only if E does. Similar result is also given for Bochner spaces L(μ,E) if 1 < p < ∞ and μ is a finite Borel measure on Ω.

1991 Abstract. A topological space X is called A-real compact, if every algebra homomorphism from A to the reals is an evaluation at some point of X, where A is an algebra of continuous functions. Our main interest lies on algebras of smooth functions. In AdR] it was shown that any separable Banach space is smoothly real compact. Here we generalize this result to a huge class of locally convex ...

We show that the Hilbert space is coarsely embeddable into any lp for 1 ≤ p < ∞. In particular, this yields new characterizations of embeddability of separable metric spaces into the Hilbert space. Coarse embeddings were defined by M. Gromov [Gr] to express the idea of inclusion in the large scale geometry of groups. G. Yu showed later that the case when a finitely generated group with a word l...

In this note the almost sure convergence of stationary, φ-mixing sequences of random variables with values in real, separable Banach spaces according to summability methods is linked to the fulfillment of a certain integrability condition generalizing and extending the results for i.i.d. sequences. Furthermore we give via Baum-Katz type results an estimate for the rate of convergence in these l...

Total subspaces in dual Banach spaces which are not norming over any infinite dimensional subspace Abstract. The main result: the dual of separable Banach space X contains a total subspace which is not norming over any infinite dimensional subspace of X if and only if X has a nonquasireflexive quotient space with the strictly singular quotient mapping. Let X be a Banach space and X * be its dua...

We compute here the Borel complexity of the relation of isometry between separable Banach spaces, using results of Gao, Kechris [1] and Mayer-Wolf [4]. We show that this relation is Borel bireducible to the universal relation for Borel actions of Polish groups.

In this paper, we study multi-step random iteration scheme with errors for a common random fixed point of a finite family of nonself asymptotically nonexpansive random mappings in real uniformly convex separable Banach spaces. The results presented in this paper extend the recent ones announced by Zhou and Wang [23] and many others. 2000 Mathematics Subject Ciassification No.: 47H09, 47H10.

In this paper, we introduce a new geometric property (A2) ∗ and we show that if a separable Banach space has property (A2) ∗ then both X and its dual X∗ have the weak fixed point property. Criteria for Orlicz spaces to have the properties (A2), (A ε 2) ∗ and (NUS∗) are given.