Document Type
Lecture
Publication Date
3-20-2015
Abstract
In the introduction of this talk, we present some classical results on the surjective linear isometries of full matrix algebras. Next, we show a substantial generalization of the classical Mazur-Ulam theorem concerning surjective isometries of normed linear spaces. It states that the surjective isometries of quite general algebraic structures (so-called point reflection geometries) locally preserve the algebraic operation, meaning that those geometric transformations necessarily have algebraic features. Using that result, we determine the surjective isometries of certain matrix structures (positive definite cone, unitary group) with respect to several important, typically non-Euclidean metrics, generalized distance measures, or divergences.
Relational Format
presentation
Recommended Citation
Molnar, Lajos, "Generalized Mazur-Ulam Theorems and Isometries of Matrix Spaces" (2015). Analysis Seminar. 8.
https://egrove.olemiss.edu/math_analysis/8
