Jacobi fields on space of positive operators

Abstract

Let A be a C *-algebra with 1 and denote by A + the set of invertible positive elements of A with its canonical connection and Finsler structure (see [2]). Then a Jacobi field J( t) along a geodesic in A + with initial conditions J(0) = 0 or DJ / dt¦ t = 0 has increasing Finsler norm for t ≥ 0.