On Orthogonal Decompositions of "Pull Back" Hermitian Holomorphic Vector Bundles

【摘要】 <正>Let f:Ω→(?)r(n,H) be a holomorphic curve, whereΩis a bounded open simple connected domain on the complex plane (?) and (?)r(n, H) the Grassman-nian manifold. Denote by Ef the "pull back" bundle induced by f. We show the uniqueness of the orthogonal decomposition for those complex bundles. As a direct application, we give a complete description of the HIR decomposition of a Cowen-Douglas operator T∈Bn(Ω). Moreover, we compute the maximal self-adjoint sub-algebra of A′(Ef) and A′(T) respectively. Finally, we fix the masa of A′(Ef) and A′(T) which depends on the HIR decomposition of Ef or T respectively.更多还原

【Abstract】 Let f:Ω→(?)r(n,H) be a holomorphic curve, whereΩis a bounded open simple connected domain on the complex plane (?) and (?)r(n, H) the Grassman-nian manifold. Denote by Ef the "pull back" bundle induced by f. We show the uniqueness of the orthogonal decomposition for those complex bundles. As a direct application, we give a complete description of the HIR decomposition of a Cowen-Douglas operator T∈Bn(Ω). Moreover, we compute the maximal self-adjoint sub-algebra of A′(Ef) and A′(T) respectively. Finally, we fix the masa of A′(Ef) and A′(T) which depends on the HIR decomposition of Ef or T respectively.更多还原