Search results for "operators"
showing 10 items of 228 documents
A unified Pietsch domination theorem
2008
In this paper we prove an abstract version of Pietsch's domination theorem which unify a number of known Pietsch-type domination theorems for classes of mappings that generalize the ideal of absolutely p-summing linear operators. A final result shows that Pietsch-type dominations are totally free from algebraic conditions, such as linearity, multilinearity, etc.
Existence theorems for m-accretive operators in Banach spaces
2005
Abstract In 1985, the second author proved a surjective result for m -accretive and ϕ -expansive mappings for uniformly smooth Banach spaces. However, in this case, we have been able to remove the uniform smoothness of the Banach space, without any additional assumption.
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.
The fixed point property for mappings admitting a center
2007
Abstract We introduce a class of nonlinear continuous mappings in Banach spaces which allow us to characterize the Banach spaces without noncompact flat parts in their spheres as those that have the fixed point property for this type of mapping. Later on, we give an application to the existence of zeroes for certain kinds of accretive operators.
Some Classes of Operators on Partial Inner Product Spaces
2012
Many families of function spaces, such as $L^{p}$ spaces, Besov spaces, amalgam spaces or modulation spaces, exhibit the common feature of being indexed by one parameter (or more) which measures the behavior (regularity, decay properties) of particular functions. All these families of spaces are, or contain, scales or lattices of Banach spaces and constitute special cases of the so-called \emph{partial inner product spaces (\pip s)} that play a central role in analysis, in mathematical physics and in signal processing (e.g. wavelet or Gabor analysis). The basic idea for this structure is that such families should be taken as a whole and operators, bases, frames on them should be defined glo…
Pietsch's factorization theorem for dominated polynomials
2007
Abstract We prove that, like in the linear case, there is a canonical prototype of a p -dominated homogeneous polynomial through which every p -dominated polynomial between Banach spaces factors.
Property (R) for Bounded Linear Operators
2011
We introduce the spectral property (R), for bounded linear operators defined on a Banach space, which is related to Weyl type theorems. This property is also studied in the framework of polaroid, or left polaroid, operators.
Non-self-adjoint resolutions of the identity and associated operators
2013
Closed operators in Hilbert space defined by a non-self-adjoint resolution of the identity $$\{X(\lambda )\}_{\lambda \in {\mathbb R}}$$ , whose adjoints constitute also a resolution of the identity, are studied. In particular, it is shown that a closed operator $$B$$ has a spectral representation analogous to the familiar one for self-adjoint operators if and only if $$B=\textit{TAT}^{-1}$$ where $$A$$ is self-adjoint and $$T$$ is a bounded inverse.
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.
On certain linear operators in spaces of ultradifferentiable functions
1996
Let ω be a weight in the sense of Braun, Meise, Taylor, which defines a non-quasianalytic class. Let H be a compact subset of ℝn. It is proved that for every function ƒ on ℝn which belongs to the non-quasianalytic (ω)-class, there is an element g of the same class which is analytic on ℝn\H and such that Dαƒ(x) = Dαg(x) for every x ∈ H and α ∈ ℕ0n. A similar result is proved for functions of the Roumieu type. Continuous linear extension operators of Whitney jets with additional properties are also obtained.