Faculty of Mathematics, Babes-Bolyai University,
1 M. Kog\u alniceanu Str., Cluj-Napoca, Romania
Abstract. Let X be a complex Banach space and let B be the unit ball of X. In this paper we obtain sufficient conditions for biholomorphic mappings on B to have parametric representation. Also we study certain properties of Loewner chains, and we obtain infinite dimensional versions of some well known univalence criteria on the unit ball of Cn.
2000 Mathematics Subject Classification. 32H02, 30C45.
Key words and phrases. Biholomorphic mapping, Loewner chains, parametric representation, univalence criteria.