Search results for "Operator"
showing 10 items of 1427 documents
Perturbations of surjective convolution operators
2002
Let μ 1 and μ 2 be (ultra)distributions with compact support which have disjoint singular supports. We assume that the convolution operator f → μ 1 *f is surjective when it acts on a space of functions or (ultra)distributions, and we investigate whether the perturbed convolution operator f→ (μ 1 + μ 2 ) * f is surjective. In particular we solve in the negative a question asked by Abramczuk in 1984.
Restricted Uniform Boundedness in Banach Spaces
2009
Precise conditions for a subset A of a Banach space X are known in order that pointwise bounded on A sequences of bounded linear functionals on X are uniformly bounded. In this paper, we study such conditions under the extra assumption that the functionals belong to a given linear subspace Γ of X *. When Γ = X *, these conditions are known to be the same ones assuring a bounded linear operator into X , having A in its image, to be onto. We prove that, for A , deciding uniform boundedness of sequences in Γ is the same property as deciding surjectivity for certain classes of operators. Keywords: Uniform boundedness; thick set; boundedness deciding set Quaestiones Mathematicae 32(2…
On the best Lipschitz extension problem for a discrete distance and the discrete ∞-Laplacian
2012
Abstract This paper concerns the best Lipschitz extension problem for a discrete distance that counts the number of steps. We relate this absolutely minimizing Lipschitz extension with a discrete ∞-Laplacian problem, which arises as the dynamic programming formula for the value function of some e -tug-of-war games. As in the classical case, we obtain the absolutely minimizing Lipschitz extension of a datum f by taking the limit as p → ∞ in a nonlocal p -Laplacian problem.
Sobolev classes of Banach space-valued functions and quasiconformal mappings
2001
We give a definition for the class of Sobolev functions from a metric measure space into a Banach space. We give various characterizations of Sobolev classes and study the absolute continuity in measure of Sobolev mappings in the “borderline case”. We show under rather weak assumptions on the source space that quasisymmetric homeomorphisms belong to a Sobolev space of borderline degree; in particular, they are absolutely continuous. This leads to an analytic characterization of quasiconformal mappings between Ahlfors regular Loewner spaces akin to the classical Euclidean situation. As a consequence, we deduce that quasisymmetric maps respect the Cheeger differentials of Lipschitz functions …
Norm, essential norm and weak compactness of weighted composition operators between dual Banach spaces of analytic functions
2017
Abstract In this paper we estimate the norm and the essential norm of weighted composition operators from a large class of – non-necessarily reflexive – Banach spaces of analytic functions on the open unit disk into weighted type Banach spaces of analytic functions and Bloch type spaces. We also show the equivalence of compactness and weak compactness of weighted composition operators from these weighted type spaces into a class of Banach spaces of analytic functions, that includes a large family of conformally invariant spaces like BMOA and analytic Besov spaces.
The Bishop–Phelps–Bollobás property for operators from c0 into some Banach spaces
2017
Abstract We exhibit a new class of Banach spaces Y such that the pair ( c 0 , Y ) has the Bishop–Phelps–Bollobas property for operators. This class contains uniformly convex Banach spaces and spaces with the property β of Lindenstrauss. We also provide new examples of spaces in this class.
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.
On generalized a-Browder's theorem
2007
We characterize the bounded linear operators T satisfying generalized a-Browder's theorem, or generalized a-Weyl's theorem, by means of localized SVEP, as well as by means of the quasi-nilpotent part H0(�I T) asbelongs to certain sets of C. In the last part we give a general framework in which generalized a-Weyl's theorem follows for several classes of operators. 1. Preliminaries. Let L(X) denote the space of bounded linear oper- ators on an infinite-dimensional complex Banach space X. For T ∈ L(X), denote by α(T) the dimension of the kernel ker T, and by β(T) the codi- mension of the range T(X). The operator T ∈ L(X) is called upper semi- Fredholm if α(T) < ∞ and T(X) is closed, and lower …
Boundaries for algebras of analytic functions on function module Banach spaces
2013
We consider the uniform algebra of continuous and bounded functions that are analytic on the interior of the closed unit ball of a complex Banach function module X. We focus on norming subsets of , i.e., boundaries, for such algebra. In particular, if X is a dual complex Banach space whose centralizer is infinite-dimensional, then the intersection of all closed boundaries is empty. This also holds in case that X is an -sum of infinitely many Banach spaces and further, the torus is a boundary.
Entire Functions of Bounded Type on Fréchet Spaces
1993
We show that holomorphic mappings of bounded type defined on Frechet spaces extend to the bidual. The relationship between holomorphic mappings of bounded type and of uniformly bounded type is discussed and some algebraic and topological properties of the space of all entire mappings of (uniformly) bounded type are proved, for example a holomorphic version of Schauder's theorem.