We study analytic families of non-compact cycles, and prove there exists an analytic space of finite dimension, which gives a universal reparametrization of such a family, under some assumptions of regularity. Then we prove an analogous statement for meromorphic families of non-compact cycles. That is a new approach to Grauert’s results about meromorphic equivalence relations.
Here we study the existence of lower and upper -estimates of sequences in some Banach sequence spaces. We also compute the sharp estimates in their basis. Finally, we give some applications to weak sequential continuity of polynomials.
The aim of this paper is to present a tool used to show that certain Banach spaces can be endowed with smooth equivalent norms. The hypothesis uses particular countable decompositions of certain subsets of , namely boundaries. Of interest is that the main result unifies two quite well known results. In the final section, some new corollaries are given.
We relate the Grothendieck inequality to the theory of vector measures and show that the integral of an inner product with respect to a bimeasure can be computed in an iterative way. We then show an application to the theory of bounded linear operators.
Emmanuele showed that if Σ is a σ-algebra of sets, X is a Banach space, and μ: Σ → X is countably additive with finite variation, then μ(Σ) is a Dunford-Pettis set. An extension of this theorem to the setting of bounded and finitely additive vector measures is established. A new characterization of strongly bounded operators on abstract continuous function spaces is given. This characterization motivates the study of the set of (sb) operators. This class of maps is used to extend results of P. Saab...
The area of research of this paper goes back to a 1930 result of H. Auerbach showing that a scalar series is (absolutely) convergent if all its zero-density subseries converge. A series in a topological vector space X is called ℒ-convergent if each of its lacunary subseries (i.e. those with ) converges. The space X is said to have the Lacunary Convergence Property, or LCP, if every ℒ-convergent series in X is convergent; in fact, it is then subseries convergent. The Zero-Density Convergence...
The duality between H1 and BMO, the space of functions of bounded mean oscillation (see [JN]), was first proved by C. Fefferman (see [F], [FS]) and then other proofs of it were obtained.In this paper we shall study such space in little more detail and we shall consider the H1-BMO duality for vector-valued functions in the more general setting of spaces of homogeneous type (see [CW]).
Let X be a Banach space. The property (∗) “the unit ball of X belongs to Baire(X, weak)” holds whenever the unit ball of X* is weak*-separable; on the other hand, it is also known that the validity of (∗) ensures that X* is weak*-separable. In this paper we use suitable renormings of and the Johnson-Lindenstrauss spaces to show that (∗) lies strictly between the weak*-separability of X* and that of its unit ball. As an application, we provide a negative answer to a question raised by K. Musiał....
For a finite and positive measure space Ω,∑,μ characterizations of weak Cauchy sequences in , the space of μ-essentially bounded vector-valued functions f:Ω → X, are presented. The fine distinction between Asplund and conditionally weakly compact subsets of is discussed.