In this talk we are concerned with the descriptions of bijective maps between the positive definite cones in operator algebras that preserve different sorts of geometric means. We mainly focus on the Kubo-Ando geometric mean and the Fiedler-Pták geometric mean. As for the former one, we present an extension of a former result of ours from the case of von Neumann factors to the case of more general algebras. As for the Fiedler-Pták geometric mean, we present the first satisfactory result that concerns the case of finite factor von Neumann algebras.

报告人简介：Molnár, Lajos（匈牙利University of Szeged）, 匈牙利塞格德大学终身教授，算子代数与量子信息科学方面的国际知名专家。曾获得匈牙利科学院学院奖，匈牙利科学院“Momentum（Lendület）”计划获奖者，匈牙利总统颁发的“匈牙利共和国功勋骑士十字勋章”，蒂博·谢莱纪念奖章。担任国际学术组织职位：国际量子结构协会理事；《Acta Scientiarum Mathematicarum》主编；《Acta Mathematica Hungarica》、《Aequationes Mathematicae》、《Journal of Mathematical Analysis and Application》、《Linear Algebra and its Applications》、《Linear and Multilinear Algebra》、《Operators and Matrices》、《Publicationes Mathematicae》期刊的编委；Springer出版的“Bolyai Society Mathematical Studies”书系编委。研究成果发表在《Comm. Math. Phys.》、《J. Funct. Anal.》等重要期刊上。