March 7, 2000 Abstract. A Banach space X is said to have the separable lifting property if for every subspace Y of X containing X and such that Y/X is separable there exists a bounded linear lifting from Y/X to Y . We show that if a sequence of Banach spaces E1, E2, . . . has the joint uniform approximation property and En is c-complemented in E∗∗ n for every n (with c fixed), then P n En 0 has...

We provide a porosity based approach to the differentiability and continuity of real valued functions on separable Banach spaces, when the function is monotone with respect to an ordering induced by a convex cone K with non-empty interior. We also show that the set of nowhere K-monotone functions has a σ-porous complement in the space of the continuous functions.

We establish sufficient conditions on the shape of a set A included in the space Lns (X, Y ) of the n-linear symmetric mappings between Banach spaces X and Y , to ensure the existence of a C-smooth mapping f : X −→ Y , with bounded support, and such that f (X) = A, provided that X admits a Csmooth bump with bounded n-th derivative and dens X = densL(X, Y ). For instance, when X is infinite-dime...

We study linear and algebraic structures in sets of bounded holomorphic functions on the ball which have large cluster at every possible point (i.e., sphere several complex variables closed unit bidual infinite dimensional case). show that this set is strongly c-algebrable for all separable Banach spaces. For specific spaces including ℓ p or duals Lorentz sequence spaces, we c-algebrability spa...

We extend the standard Fourier multiplier result to square integrable functions with values in (possibly nonseparable) Hilbert spaces. As a corollary, we extend the standard Hardy class boundary trace result to H (even Nevanlinna or bounded type) functions whose values are bounded linear operators between Hilbert spaces. Both results have been well-known in the case that the Hilbert spaces are ...

We work in the set theory without the axiom of choice: ZF. Though the Hahn-Banach theorem cannot be proved in ZF, we prove that every Gâteauxdifferentiable uniformly convex Banach space E satisfies the following continuous Hahn-Banach property: if p is a continuous sublinear functional on E, if F is a subspace of E, and if f : F → R is a linear functional such that f ≤ p|F , then there exists a...

We extend the well-known characterizations of convergence in spaces $l_p$ ($1\le p<\infty$) $p$-summable sequence and $c_0$ vanishing sequences to a general characterization Banach space with Schauder basis obtain as instant corollaries an infinite-dimensional separable Hilbert $c$ convergent sequences.

On a reflexive Banach space X , if an operator T admits a functional calculus for the absolutely continuous functions on its spectrum σ(T ) ⊆ R, then this functional calculus can always be extended to include all the functions of bounded variation. This need no longer be true on nonreflexive spaces. In this paper, it is shown that on most classical separable nonreflexive spaces, one can constru...

A general Fatou Lemma is established for a sequence of Gelfand integrable functions from a vector Loeb space to the dual of a separable Banach space or, with a weaker assumption on the sequence, a Banach lattice. A corollary sharpens previous results in the …nite dimensional setting even for the case of scalar measures. Counterexamples are presented to show that the results obtained here are sh...

In this work, we present an application of Newton’s method for solving nonlinear equations in Banach spaces to a particular problem: the approximation inverse operators that appear solution Fredholm integral equations. Therefore, construct iterative with quadratic convergence does not use either derivatives or operators. Consequently, new procedure is especially useful non-homogeneous first kin...