conference paper
Dirac masses and isometric rigidity
published
yes
Gyorgy Pal
Geher
author
Tamas
Titkos
author
Daniel
Virosztek
author 48DB45DA-F248-11E8-B48F-1D18A9856A87
LaEr
department
Research on isometries as preserver problems and related topics
The aim of this short note is to expound one particular issue that was discussed during the talk [10] given at the symposium ”Researches on isometries as preserver problems and related topics” at Kyoto RIMS. That is, the role of Dirac masses by describing the isometry group of various metric spaces of probability measures. This article is of survey character, and it does not contain any essentially new results.From an isometric point of view, in some cases, metric spaces of measures are similar to C(K)-type function spaces. Similarity means here that their isometries are driven by some nice transformations of the underlying space. Of course, it depends on the particular choice of the metric how nice these transformations should be. Sometimes, as we will see, being a homeomorphism is enough to generate an isometry. But sometimes we need more: the transformation must preserve the underlying distance as well. Statements claiming that isometries in questions are necessarily induced by homeomorphisms are called Banach-Stone-type results, while results asserting that the underlying transformation is necessarily an isometry are termed as isometric rigidity results.As Dirac masses can be considered as building bricks of the set of all Borel measures, a natural question arises:Is it enough to understand how an isometry acts on the set of Dirac masses? Does this action extend uniquely to all measures?In what follows, we will thoroughly investigate this question.
Research Institute for Mathematical Sciences, Kyoto University2019Kyoto, Japan
eng
Kyoto RIMS Kôkyûroku
212534-41
G.P. Geher, T. Titkos, D. Virosztek, in:, Kyoto RIMS Kôkyûroku, Research Institute for Mathematical Sciences, Kyoto University, 2019, pp. 34–41.
Geher GP, Titkos T, Virosztek D. 2019. Dirac masses and isometric rigidity. Kyoto RIMS Kôkyûroku. Research on isometries as preserver problems and related topics vol. 2125. 34–41.
Geher GP, Titkos T, Virosztek D. Dirac masses and isometric rigidity. In: <i>Kyoto RIMS Kôkyûroku</i>. Vol 2125. Research Institute for Mathematical Sciences, Kyoto University; 2019:34-41.
Geher, Gyorgy Pal, et al. “Dirac Masses and Isometric Rigidity.” <i>Kyoto RIMS Kôkyûroku</i>, vol. 2125, Research Institute for Mathematical Sciences, Kyoto University, 2019, pp. 34–41.
Geher, G. P., Titkos, T., & Virosztek, D. (2019). Dirac masses and isometric rigidity. In <i>Kyoto RIMS Kôkyûroku</i> (Vol. 2125, pp. 34–41). Kyoto, Japan: Research Institute for Mathematical Sciences, Kyoto University.
Geher, Gyorgy Pal, Tamas Titkos, and Daniel Virosztek. “Dirac Masses and Isometric Rigidity.” In <i>Kyoto RIMS Kôkyûroku</i>, 2125:34–41. Research Institute for Mathematical Sciences, Kyoto University, 2019.
G. P. Geher, T. Titkos, and D. Virosztek, “Dirac masses and isometric rigidity,” in <i>Kyoto RIMS Kôkyûroku</i>, Kyoto, Japan, 2019, vol. 2125, pp. 34–41.
70352019-11-18T15:39:53Z2019-12-02T13:33:50Z