摘要 : In [3], M. J. Cowen and R. G. Douglas prove that the adjoint of a Hilbert space operator T is in the class ${\mathcal{B}}_n(\Omega)$ if and only if T is unitarily equivalent with the operator M z </sub> on a Hilbert space ${\mathc... 展开 In [3], M. J. Cowen and R. G. Douglas prove that the adjoint of a Hilbert space operator T is in the class ${\mathcal{B}}_n(\Omega)$ if and only if T is unitarily equivalent with the operator M z </sub> on a Hilbert space ${\mathcal{H}}\,{\rm of}\,{\mathbb{C}}^n$ -valued analytic functions, where M z </sub> denotes the operator of multiplication by the independent variable. The proof involves holomorphic vector bundles and Grauert’s theorem. 收起