Isometries and Toeplitz operators of Bergman space of bounded symmetric domains

Abstract In this paper we completely characterize the isometries of Bergman space L a p ( Ω ) ( 0 ⩽ p ∞ , p ≠ 2 ) of bounded symmetric domains. We also prove that a pair of Toeplitz operators T f and T g on L a p ( Ω ) ( 0 p ∞ , p ≠ 2 ) is isometric equivalence if and only if there is a τ ∈ Aut ( Ω ) , such that g = f ○ τ , where Aut ( Ω ) is the automorphism group of Ω .