g-Loewner chains, Bloch functions and extension operators into the family of locally biholomorphic mappings in infinite dimensional spaces

Abstract

In this paper, we survey recent results obtained by the authors
on the preservations of the first elements of (g-) Loewner chains and
the Bloch mappings by the Roper-Suffridge type extension operators,
the Muir type extension operators and the Pfaltzgraff-Suffridge type
extension operators into the mappings on the domains in the complex
Banach spaces.