26 citations · 76 across the 23 of their papers we have counts for
24 papers
Some observations on transitivity of Lipschitz operators
Christian Bargetz, Leon Kügler
The universal property of the Lipschitz-free spaces allows for the linearisation of a base point preserving Lipschitz map to a bounded linear operator $T_f\colon \…
On extremal nonexpansive mappings
Christian Bargetz, Michael Dymond, Katriin Pirk
We study the extremality of nonexpansive mappings on a nonempty bounded closed and convex subset of a normed space (therein specific Banach spaces). We show that surjective isometr…
Continuous operators from spaces of Lipschitz functions
Christian Bargetz, Jerzy Kąkol, Damian Sobota
We study the existence of continuous (linear) operators from the Banach spaces $\mbox{Lip}_0(M)$ of Lipschitz functions on infinite metric spaces vanishing at a distinguished p…
Tilings of the Hyperbolic Space and Lipschitz Functions
Christian Bargetz, Franz Luggin, Tommaso Russo
We use a special tiling for the hyperbolic -space for to construct an (almost) explicit isomorphism between the Lipschitz-free space $\mathcal{F}(\mathb…
Observations on the metric projection in finite dimensional Banach spaces
Christian Bargetz, Franz Luggin
We consider the method of alternating (metric) projections for pairs of linear subspaces of finite dimensional Banach spaces. We investigate the size of the set of points for which…
Homogeneous isosceles-free spaces
Christian Bargetz, Adam Bartoš, Wiesław Kubiś +1
We study homogeneity aspects of metric spaces in which all triples of distinct points admit pairwise different distances; such spaces are called isosceles-free. In particular, we c…
On generic convergence of successive approximations of mappings with convex and compact point images
Christian Bargetz, Emir Medjic, Katriin Pirk
We study the generic behavior of the method of successive approximations for set-valued mappings in separable Banach spaces. We consider the case of nonexpansive mappings with conv…
Generic properties of nonexpansive mappings on unbounded domains
Christian Bargetz, Simeon Reich, Daylen Thimm
We investigate typical properties of nonexpansive mappings on unbounded complete hyperbolic metric spaces. For two families of metrics of uniform convergence on bounded sets, we sh…
Projective descriptions of spaces of functions and distributions
Christian Bargetz, Eduard A. Nigsch, Norbert Ortner
We present projective descriptions of classical spaces of functions and distributions. More precisely, we provide descriptions of these spaces by semi-norms which are defined by a…
On complemented copies of the space in spaces
Christian Bargetz, Jerzy Kąkol, Damian Sobota
We study the question for which Tychonoff spaces and locally convex spaces the space of continuous -valued functions on contains a complemented copy of th…
Sequence space representations for spaces of smooth functions and distributions via Wilson bases
Christian Bargetz, Andreas Debrouwere, Eduard A. Nigsch
We provide explicit sequence space representations for the test function and distribution spaces occurring in the Valdivia-Vogt structure tables by making use of Wilson bases gener…
On angles, projections and iterations
Christian Bargetz, Jona Klemenc, Simeon Reich +1
We investigate connections between the geometry of linear subspaces and the convergence of the alternating projection method for linear projections. The aim of this article is twof…
On the existence of fixed points for typical nonexpansive mappings on spaces with positive curvature
Christian Bargetz, Michael Dymond, Emir Medjic +1
We show that the typical nonexpansive mapping on a small enough subset of a CAT()-space is a contraction in the sense of Rakotch. By typical we mean that the set of nonexpansive…
On the rate of convergence of iterated Bregman projections and of the alternating algorithm
Christian Bargetz, Emir Medjic
We study the alternating algorithm for the computation of the metric projection onto the closed sum of two closed subspaces in uniformly convex and uniformly smooth Banach spaces.…
Generic Convergence of Sequences of Successive Approximations in Banach Spaces
Christian Bargetz, Simeon Reich
We study the generic behavior of the method of successive approximations for set-valued mappings in Banach spaces. We consider, in particular, the case of those set-valued mappings…
Linear Convergence Rates for Extrapolated Fixed Point Algorithms
Christian Bargetz, Victor I. Kolobov, Simeon Reich +1
We establish linear convergence rates for a certain class of extrapolated fixed point algorithms which are based on dynamic string-averaging methods in a real Hilbert space. This a…
A simpler description of the -topologies on the spaces , ,
Christian Bargetz, Eduard A. Nigsch, Norbert Ortner
The -topologies on the spaces , and are defined by a neighbourhood basis consisting of polars of absolutely convex and compact subsets o…
Convergence Properties of Dynamic String Averaging Projection Methods in the Presence of Perturbations
Christian Bargetz, Simeon Reich, Rafał Zalas
Assuming that the absence of perturbations guarantees weak or strong convergence to a common fixed point, we study the behavior of perturbed products of an infinite family of nonex…
Pivot duality of universal interpolation and extrapolation spaces
Christian Bargetz, Sven-Ake Wegner
It is a widely used method, for instance in perturbation theory, to associate with a given C0-semigroup its so-called interpolation and extrapolation spaces. In the model case of t…
A separable Fréchet space of almost universal disposition
C. Bargetz, J. Kakol, W. Kubiś
The Gurari\uı space is the unique separable Banach space which is of almost universal disposition for finite-dimensional Banach spaces, which means that for every $\va…
Porosity Results for Sets of Strict Contractions on Geodesic Metric Spaces
Christian Bargetz, Michael Dymond, Simeon Reich
We consider a large class of geodesic metric spaces, including Banach spaces, hyperbolic spaces and geodesic -spaces, and investigate the space of nonexpansive map…
Kernel Identities and Vectorial Regularization
Christian Bargetz, Norbert Ortner
We present the method of "vectorial regularization" to prove kernel identities. This method is applied to derive both known kernel identities, e.g. $\dot{\mathcal{B}}_{xy}=\dot{\ma…
Convolvability and regularization of distributions
C. Bargetz, E. A. Nigsch, N. Ortner
We apply L.~Schwartz' theory of vector valued distributions in order to simplify, unify and generalize statements about convolvability of distributions, their regularization proper…
σ-Porosity of the set of strict contractions in a space of non-expansive mappings
Christian Bargetz, Michael Dymond
We consider the space of non-expansive mappings on a bounded, closed and convex subset of a Banach space equipped with the metric of uni- form convergence. We show that the set of…