Hermitian Jordan triple systems and the automorphisms of bounded symmetric domains. (English) Zbl 0810.46075

Kaup, Wilhelm

González, Santos (ed.), Non-associative algebra and its applications. 3rd international conference, Oviedo, Spain, July 12th-17th, 1993. Dordrecht: Kluwer Academic Publishers. Math. Appl., Dordr. 303, 204-214 (1994).

Summary: We describe bounded symmetric domains in complex Banach spaces and their biholomorphic automorphisms in terms of the underlying \(\text{JB}^*\)-triple structures. Of particular interest in this context is the square root of a certain Bergman operator – we give a new description of this square root as exponential of a Hermitian operator which gives better norm estimates. We do not give full proofs. These will appear elsewhere.
For the entire collection see [Zbl 0801.00022].

MSC:

46L70	Nonassociative selfadjoint operator algebras
17C65	Jordan structures on Banach spaces and algebras

Keywords:

bounded symmetric domains; biholomorphic automorphisms; \(\text{JB}^*\)-triple structures; Bergman operator; square root; exponential of a Hermitian operator