Bloch functions on bounded symmetric domains

We introduce and characterize Bloch functions on bounded symmetric domains, which may be infinite dimensional, by extending several well-known equivalent conditions for Bloch functions on the open unit disc U in C. We also generalize a number of results concerning Bloch functions on U to bounded symmetric domains. Given a holomorphic mapping φ between bounded symmetric domains BX and BY, we derive criteria for boundedness and compactness of the composition operator Cφ between the Bloch spaces B(BY) and B(BX), extending several known results for finite dimensional domains.