Molnar, Lajos, Kolokvij maj 2018

Iz MaFiRaWiki

Surjective isometries are likely the most important 'symmetries' of metric spaces. When the underlying space is also equipped with some compatible algebraic structure, it frequently turns out that the (surjective) isometries are closely related to corresponding algebraic isomorphisms.

In this talk we are concerned with that phenomenon in areas of linear algebra and functional analysis. In the first part of the talk we present some classical results related to matrix algebras (probably mentioning their infinite dimensional generalizations, too). In the second part we consider some particular non-linear problems on the positive definite cone in matrix algebras and explain how certain multiplicative or order structures and their isomorphisms help to characterize the isometries with respect to important metrics. We will comment on the infinite dimensional extensions, too.

Osebna orodja