Search results for "BANACH SPACE"

Complete weights andv-peak points of spaces of weighted holomorphic functions

2006

We examine the geometric theory of the weighted spaces of holomorphic functions on bounded open subsets ofC n ,C n ,H v (U) and\(H_{v_o } (U)\), by finding a lower bound for the set of weak*-exposed and weak*-strongly exposed points of the unit ball of\(H_{v_o } (U)'\) and give necessary and sufficient conditions for this set to be naturally homeomorphic toU. We apply these results to examine smoothness and strict convexity of\(H_{v_o } (U)\) and\(H_v (U)\). We also investigate whether\(H_{v_o } (U)\) is a dual space.

Fréchet Spaces of Holomorphic Functions without Copies of l 1

1996

Let X be a Banach space. Let Hw*(X*) the Frechet space whose elements are the holomorphic functions defined on X* whose restrictions to each multiple mB(X*), m = 1,2, …, of the closed unit ball B(X*) of X* are continuous for the weak-star topology. A fundamental system of norms for this space is the supremum of the absolute value of each element of Hw*(X*) in mB(X*), m = 1,2,…. In this paper we construct the bidual of l1 when this space contains no copy of l1. We also show that if X is an Asplund space, then Hw*(X*) can be represented as the projective limit of a sequence of Banach spaces that are Asplund.

On the Unit Ball of Operator-valued H 2-functions

2009

Let X be a complex Banach space and let H 2 (\( \mathbb{D} \), X) denote the space of X-valued analytic functions in the unit disc such that $$ \mathop {sup}\limits_{0 < r < 1} \int_0^{2\pi } {\left\| {F\left( {re^{it} } \right)} \right\|^2 \frac{{dt}} {{2\pi }} < \infty .} $$ It is shown that a function F belongs to the unit ball of H 2 ( \( \mathbb{D} \), X) if and only if there exist f∈H ∞ (\( \mathbb{D} \), X) and ϕ∈H ∞ (\( \mathbb{D} \)) such that $$ \left\| {f\left( z \right)} \right\|^2 + \left| {\varphi \left( z \right)} \right|^2 \leqslant 1 and F\left( z \right) = \frac{{f\left( z \right)}} {{1 - z\varphi \left( z \right)}} $$ for |z| < 1.

A note on Fréchet and approximate subdifferentials of composite functions

1994

The aim of this note is to present in the reflexive Banach space setting a natural and simple proof of the formula of the approximate subdifferential of a composite function.

Third-order iterative methods without using any Fréchet derivative

2003

AbstractA modification of classical third-order methods is proposed. The main advantage of these methods is they do not need to evaluate any Fréchet derivative. A convergence theorem in Banach spaces, just assuming the second divided difference is bounded and a punctual condition, is analyzed. Finally, some numerical results are presented.

Bounded approximation properties via integral and nuclear operators

2010

Published version of an article in the journal:Proceedings of the American Mathematical Society. Also available from the publisher, Open Access

Approximations of Parabolic Equations at the Vicinity of Hyperbolic Equilibrium Point

2014

This article is devoted to the numerical analysis of the abstract semilinear parabolic problem u′(t) = Au(t) + f(u(t)), u(0) = u 0, in a Banach space E. We are developing a general approach to establish a discrete dichotomy in a very general setting and prove shadowing theorems that compare solutions of the continuous problem with those of discrete approximations in space and time. In [3] the discretization in space was constructed under the assumption of compactness of the resolvent. It is a well-known fact (see [10, 11]) that the phase space in the neighborhood of the hyperbolic equilibrium can be split in a such way that the original initial value problem is reduced to initial value prob…

On Boundary Conditions for Wedge Operators on Radial Sets

2008

We present a theorem about calculation of fixed point index for k-$\psi$-contractive operators with 0 < k <1 defined on a radial set of a wedge of an infinite dimensional Banach space. Then results on the existence of eigenvectors and nonzero fixed points are obtained.

Weak convergence theorems for asymptotically nonexpansive mappings and semigroups

2001

Delta- and Daugavet points in Banach spaces

2020

AbstractA Δ-pointxof a Banach space is a norm-one element that is arbitrarily close to convex combinations of elements in the unit ball that are almost at distance 2 fromx. If, in addition, every point in the unit ball is arbitrarily close to such convex combinations,xis a Daugavet point. A Banach spaceXhas the Daugavet property if and only if every norm-one element is a Daugavet point. We show that Δ- and Daugavet points are the same inL1-spaces, inL1-preduals, as well as in a big class of Müntz spaces. We also provide an example of a Banach space where all points on the unit sphere are Δ-points, but none of them are Daugavet points. We also study the property that the unit ball is the clo…