Geometric operator inequalities
In a given \(C^*\)-algebra there are several interesting subsets (e.g., the set of idempotent elements, the set of selfadjoint invertible elements, the set of nilpotent elements of a given order, the similarity and unitary orbits of elements etc.) that have a differentiable structure and in which the length of curves is measured by means of a Finsler metric. The construction of this metric on the given such set depends on some operator inequalities. The paper contains a fairly complete discussion relating the differential geometry and such operator inequalities. The authors also prove some spectral properties of transformations related to these inequalities.
similarity and unitary orbits of elements
scientific article; zbMATH DE number 1026444
scientific article