• Corpus ID: 222291716

On a theorem about Mosco convergence in Hadamard spaces

  title={On a theorem about Mosco convergence in Hadamard spaces},
  author={Arian Berdellima},
  journal={arXiv: Functional Analysis},
Let $(f^n),f$ be a sequence of proper closed convex functions defined on a Hadamard space. We show that the convergence of proximal mappings $J^n_{\lambda}x$ to $J_{\lambda}x$, under certain additional conditions, imply Mosco convergence of $f^n$ to $f$. This result is a converse to a theorem of Bacak about Mosco convergence in Hadamard spaces. 

Figures from this paper


Familles d'opérateurs maximaux monotones et mesurabilité
SummaryThis paper is devoted to the study of family of maximal monotone operators in Hilbert spaces. The first part deals with convergence of such sequences in resolvent's sense, the second one with
Old and new challenges in Hadamard spaces
Hadamard spaces have traditionally played important roles in geometry and geometric group theory. More recently, they have additionally turned out to be a suitable framework for convex analysis,
Convex Analysis and Optimization in Hadamard Spaces
This book gives a first systematic account on the subject of convex analysis and optimization in Hadamard spaces. It is primarily aimed at both graduate students and researchers in analysis and
Metric Structures for Riemannian and Non-Riemannian Spaces
Length Structures: Path Metric Spaces.- Degree and Dilatation.- Metric Structures on Families of Metric Spaces.- Convergence and Concentration of Metrics and Measures.- Loewner Rediscovered.-
A Course in Metric Geometry
Preface This book is not a research monograph or a reference book (although research interests of the authors influenced it a lot)—this is a textbook. Its structure is similar to that of a graduate
Metric Spaces of Nonpositive Curvature
  • A Series of Comprehensive Studies in Mathematics,
  • 1999
Convex Analysis, Princeton Landmarks in Mathematics
  • 1970