Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 1

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: minimal curves

Sortuj według:

Ogranicz wyniki do:

Sphere and projective space of a C*-algebra with a faithful state

Antunez Andrea C.

Demonstratio Mathematica

2019

Vol. 52, nr 1

410--427

Let A be a unital C*-algebra with a faithful state φ. We study the geometry of the unit sphere Sφ = {x∈A : φ(x*x) = 1} and the projective space Pφ = Sφ/T. These spaces are shown to be smooth manifolds and homogeneous spaces of the group Uφ(A) of isomorphisms acting in A which preserve the inner product induced by φ, which is a smooth Banach-Lie group. An important role is played by the theory of operators in Banach spaces with two norms, as developed by M.G. Krein and P. Lax. We define a metric in Pφ, and prove the existence of minimal geodesics, both with given initial data, and given endpoints.