Search results for "rete"

Weighted Banach spaces of entire functions

1994

THE POLYNOMIAL NUMERICAL INDEX OF A BANACH SPACE

2006

AbstractIn this paper, we introduce the polynomial numerical index of order $k$ of a Banach space, generalizing to $k$-homogeneous polynomials the ‘classical’ numerical index defined by Lumer in the 1970s for linear operators. We also prove some results. Let $k$ be a positive integer. We then have the following:(i) $n^{(k)}(C(K))=1$ for every scattered compact space $K$.(ii) The inequality $n^{(k)}(E)\geq k^{k/(1-k)}$ for every complex Banach space $E$ and the constant $k^{k/(1-k)}$ is sharp.(iii) The inequalities$$ n^{(k)}(E)\leq n^{(k-1)}(E)\leq\frac{k^{(k+(1/(k-1)))}}{(k-1)^{k-1}}n^{(k)}(E) $$for every Banach space $E$.(iv) The relation between the polynomial numerical index of $c_0$, $l…

Lipschitz operator ideals and the approximation property

2016

[EN] We establish the basics of the theory of Lipschitz operator ideals with the aim of recovering several classes of Lipschitz maps related to absolute summability that have been introduced in the literature in the last years. As an application we extend the notion and main results on the approximation property for Banach spaces to the case of metric spaces. (C) 2015 Elsevier Inc. All rights reserved.

Property (w) and perturbations

2007

A bounded linear operator T ∈ L(X) defined on a Banach space X satisfies property (w), a variant of Weyl’s theorem, if the complement in the approximate point spectrum σa(T ) of the Weyl essential approximate spectrum σwa(T ) coincides with the set of all isolated points of the spectrum which are eigenvalues of finite multiplicity. In this note, we study the stability of property (w), for a bounded operator T acting on a Banach space, under perturbations by finite rank operators, by nilpotent operator and quasi-nilpotent operators commuting with T .

An exact and efficient approach for computing a cell in an arrangement of quadrics

2006

AbstractWe present an approach for the exact and efficient computation of a cell in an arrangement of quadric surfaces. All calculations are based on exact rational algebraic methods and provide the correct mathematical results in all, even degenerate, cases. By projection, the spatial problem is reduced to the one of computing planar arrangements of algebraic curves. We succeed in locating all event points in these arrangements, including tangential intersections and singular points. By introducing an additional curve, which we call the Jacobi curve, we are able to find non-singular tangential intersections. We show that the coordinates of the singular points in our special projected plana…

Fixed-Point Theorems in Complete Gauge Spaces and Applications to Second-Order Nonlinear Initial-Value Problems

2013

We establish fixed-point results for mappings and cyclic mappings satisfying a generalized contractive condition in a complete gauge space. Our theorems generalize and extend some fixed-point results in the literature. We apply our obtained results to the study of existence and uniqueness of solution to a second-order nonlinear initial-value problem.

Remarks on G-Metric Spaces

2013

In 2005, Mustafa and Sims (2006) introduced and studied a new class of generalized metric spaces, which are called G-metric spaces, as a generalization of metric spaces. We establish some useful propositions to show that many fixed point theorems on (nonsymmetric) G-metric spaces given recently by many authors follow directly from well-known theorems on metric spaces. Our technique can be easily extended to other results as shown in application.

A theorem of insertion and extension of functions for normal spaces

1993

Symplectic automorphisms of prime order on K3 surfaces

2006

The aim of this paper is to study algebraic K3 surfaces (defined over the complex number field) with a symplectic automorphism of prime order. In particular we consider the action of the automorphism on the second cohomology with integer coefficients. We determine the invariant sublattice and its perpendicular complement, and show that the latter coincides with the Coxeter-Todd lattice in the case of automorphism of order three. We also compute many explicit examples, with particular attention to elliptic fibrations.

From quantale algebroids to topological spaces: Fixed- and variable-basis approaches

2010

Using the category of quantale algebroids the paper considers a generalization of the classical Papert-Papert-Isbell adjunction between the categories of topological spaces and locales to partial algebraic structures. It also provides a single framework in which to treat the concepts of quasi, standard and stratified fuzzy topology.