IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
Infinitely many minimal curves joining arbitrarily close points in homogeneous spaces of the unitary group of a C*-algebra
Autor/es:
ANDRUCHOW, E.; MATA-LORENZO, L.; MENDOZA, A.; RECHT, L.; VARELA, A.
Revista:
REVISTA DE LA UNIóN MATEMáTICA ARGENTINA
Editorial:
UMA
Referencias:
Año: 2006 vol. 46 p. 113 - 113
ISSN:
0041-6932
Resumen:
In this paper, we give an example of a homogeneous space of the unitary group of a C*-algebra which presents a remarkable phenomenon. Namely, in its natural Finsler metric there are infinitely many minimal curves joining arbitrarily close points. More precisely the homogeneous space will be called P. The unitary group U of a C*-algebra A acts transitively on the left on P. The action is denoted by L_u(p), for u in U and p in P. The isotropy  {u inU / L_u(p)  equals p} will be the unitary group of a C*-subalgebra B of A. The Finsler norm in P is naturally defined for X in (TP)p by |X|p= inf |Z + b|, for all b in B antihermitian  where Z in A is an antihermitian that projects to X in the quotient A_ah/B_ah which is identified to the tangent space (TP)p.