Search results for "Linear"
showing 10 items of 7165 documents
The support localization property of the strongly embedded subspaces of banach function spaces
2015
[EN] Motivated by the well known Kadec-Pelczynski disjointifcation theorem, we undertake an analysis of the supports of non-zero functions in strongly embedded subspaces of Banach functions spaces. The main aim is to isolate those properties that bring additional information on strongly embedded subspaces. This is the case of the support localization property, which is a necessary condition fulflled by all strongly embedded subspaces. Several examples that involve Rademacher functions, the Volterra operator, Lorentz spaces or Orlicz spaces are provided.
Hoffman's Error Bound, Local Controllability, and Sensitivity Analysis
2000
Our aim is to present sufficient conditions ensuring Hoffman's error bound for lower semicontinuous nonconvex inequality systems and to analyze its impact on the local controllability, implicit function theorem for (non-Lipschitz) multivalued mappings, generalized equations (variational inequalities), and sensitivity analysis and on other problems like Lipschitzian properties of polyhedral multivalued mappings as well as weak sharp minima or linear conditioning. We show how the information about our sufficient conditions can be used to provide a computable constant such that Hoffman's error bound holds. We also show that this error bound is nothing but the classical Farkas lemma for linear …
Fixed point results on metric and partial metric spaces via simulation functions
2015
We prove existence and uniqueness of fixed point, by using a simulation function and a lower semi-continuous function in the setting of metric space. As consequences of this study, we deduce several related fixed point results, in metric and partial metric spaces. An example is given to support the new theory.
On ideals of polynomials and multilinear mappings between Banach spaces
2003
It is shown that for every quasi-normed ideal ${\cal Q}$ of n-homogeneous continuous polynomials between Banach spaces there is a quasi-normed ideal ${\cal A}$ of n-linear continuous mappings ${\cal A}$ such that $q \in {\cal Q}$ if and only if the associated n-linear mapping $\check{q}$ of q is in ${\cal A}$.
Weakly compact multilinear mappings
1997
The notion of Arens regularity of a bilinear form on a Banach space E is extended to continuous m-linear forms, in such a way that the natural associated linear mappings, E→L (m−1E) and (m – l)-linear mappings E × … × E → E', are all weakly compact. Among other applications, polynomials whose first derivative is weakly compact are characterized.
A multilinear Lindenstrauss theorem
2006
Abstract We show that the set of N -linear mappings on a product of N Banach spaces such that all their Arens extensions attain their norms (at the same element) is norm dense in the space of all bounded N -linear mappings.
Domination spaces and factorization of linear and multilinear summing operators
2015
[EN] It is well known that not every summability property for multilinear operators leads to a factorization theorem. In this paper we undertake a detailed study of factorization schemes for summing linear and nonlinear operators. Our aim is to integrate under the same theory a wide family of classes of mappings for which a Pietsch type factorization theorem holds. Our construction includes the cases of absolutely p-summing linear operators, (p, sigma)-absolutely continuous linear operators, factorable strongly p-summing multilinear operators, (p(1), ... , p(n))-dominated multilinear operators and dominated (p(1), ... , p(n); sigma)-continuous multilinear operators.
Restricted weak type on maximal linear and multilinear integral maps
2006
It is shown that multilinear operators of the form T ( f 1 , . . . , f k ) ( x ) T(f_1,...,f_k)(x) = ∫ R n K ( x , y 1 , . . . , y k ) f 1 ( y 1 ) . . . f k ( y k ) d y 1 . . . d y k =\!\int _{\mathbb {R}^n}\!K(x,y_1,...,y_k)f_1(y_1)... f_k(y_k)dy_1...dy_k of restricted weak type ( 1 , . . . , 1 , q ) (1,...,1,q) are always of weak type ( 1 , . . . , 1 , q ) (1,...,1,q) whenever the map x → K x x\to K_x is a locally integrable L 1 ( R n ) L^1(\mathbb {R}^n) -valued function.
Summability and estimates for polynomials and multilinear mappings
2008
Abstract In this paper we extend and generalize several known estimates for homogeneous polynomials and multilinear mappings on Banach spaces. Applying the theory of absolutely summing nonlinear mappings, we prove that estimates which are known for mappings on l p spaces in fact hold true for mappings on arbitrary Banach spaces.
The λ-Error Order in Multivariate Interpolation
2005
The aim of this article is to introduce and to study a generalization of the error order of interpolation, named λ – error order of interpolation. This generalization makes possible a deeper analysis of the error in the interpolation process. We derived the general form of the λ – error order of interpolation and then we applied it for many choices of the functional λ.