Pseudodistances invariantes sur les domaines d’un espace localement convexe. (Invariant pseudodistances on domains of a locally convex space). (French) Zbl 0603.46052

Dineen, Seán; Timoney, Richard M.; Vigué, Jean-Pierre

Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 12, 515-529 (1985).

The authors prove that the Kobayashi and Carathéodory invariant metrics (and infinitesimal metrics) coincide on a convex domain in a locally convex space. Applications include showing the existence of geodesics (in the sense of Vesentini) in convex domains of a reflexive Banach space.

MSC:

46G20	Infinite-dimensional holomorphy
32A07	Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube) (MSC2010)

Keywords:

Kobayashi and Carathéodory invariant metrics; infinitesimal metrics; convex domain in a locally convex space; existence of geodesics

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