Chu Cho-Ho. Bounded Symmetric Domains in Banach Spaces

World Scientific, 2020. — 393 p. — ISBN 9789811214103; 9789811214110 9789811214127."This timely book exposes succinctly recent advances in the geometric and analytic theory of bounded symmetric domains. A unique feature is the unified treatment of both finite and infinite dimensional symmetric domains, using Jordan theory in tandem with Lie theory. The highlights include a generalized Riemann mapping theorem, which realizes a bounded symmetric domain as the open unit ball of a complex Banach spaceHolomorphic maps in Banach spaces.
Banach manifolds.
Symmetric Banach manifolds.
Jordan and Lie algebraic structures.
Jordan algebras.
Jordan triple systems.
Lie algebras and Tits-Kantor-Koecher construction.
Jordan and Lie structures in Banach spaces.
Cartan factors.
Bounded symmetric domains.
Algebraic structures of symmetric manifolds.
Realisation of bounded symmetric domains.
Rank of a bounded symmetric domain.
Boundary structures 3.5 Invariant metrics, Schwarz lemma and dynamics.
Siegel domains.
Holomorphic homogeneous regular domains.
Classification.
Function theory.
The class S.
Bloch constant and Bloch maps.
Banach spaces of Bloch functions.
Composition operators.