Abstract: In this paper, we prove that the generalized Roper-Suffridge extension operator can be embedded in Loewner chains on the unit ball in Hibert spaces, and obtain the fact that the operator keeps the properties of almost spirallike mapping of type β and other α,almost starlikeness of order α, spirallikeness of type β and starlikeness.

Key words: generalized Roper-Suffridge extension operator, Lowewner chains, almost spirallike mapping of type β and order α