Search results for " Operator"
showing 10 items of 931 documents
Existence of fixed points for the sum of two operators
2010
The purpose of this paper is to study the existence of fixed points for the sum of two nonlinear operators in the framework of real Banach spaces. Later on, we give some examples of applications of this type of results (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Some Nonlinear Methods in Fréchet Operator Rings and Ψ*-Algebras
1995
Two different inverse function theorems, one of Nash-Moser type, the other due to H. Omori, are extended to obtain special surjectivity results in locally convex and locally pseudo-convex Frechet algebras generated by group actions and derivations. In particular, the following factorization problem is discussed. Let Ψ be a locally pseudo-convex Frechet algebra with unit e and T+ : Ψ Ψ a continuous linear operator. Does there exist a neighborhood U of 0 such that the equation where T- = IΨ- T, has a solution x ∈ Ψ for every y ∈ U?
QUASI *-ALGEBRAS OF OPERATORS AND THEIR APPLICATIONS
1995
The main facts of the theory of quasi*-algebras of operators acting in a rigged Hilbert space are reviewed. The particular case where the rigged Hilbert space is generated by a self-adjoint operator in Hilbert space is examined in more details. A series of applications to quantum theories are discussed.
Generalized iterated function systems on the spacel∞(X)
2014
Abstract In the last decades there has been a current effort to extend the classical Hutchinson theory of iterated function systems composed by contractions on a metric space X into itself to more general spaces and infinitely many mappings. In this paper we consider the (countable) iterated function systems consisting of some generalized contractions on the product space X I into X , where I is an arbitrary set of natural numbers. Some approximations of the attractors of the respective iterated function systems are given.
Extensions and intentions in the rough set theory
1998
Abstract The approach to rough set theory proposed in this paper is based on the mutual correspondence of the concepts of extension and intension. It is different from the well-known approaches in the literature in that the upper approximations and the lower approximations of ‘unknown’ sets are considered as certain families of ‘known’ sets. This approach makes it possible to formulate necessary and sufficient conditions for the existence of operations on rough sets, which are analogous to classical operations on sets. The basic results presented in this paper, based on certain ideas of the second author, were formulated by the first author in his doctoral dissertation prepared under the su…
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.