Based on locally compact perturbations of the identity map similar to the Fredholm structures on real Banach manifolds, complex manifolds with inverse mapping theorem as part of the defintion are proposed. Standard to...Based on locally compact perturbations of the identity map similar to the Fredholm structures on real Banach manifolds, complex manifolds with inverse mapping theorem as part of the defintion are proposed. Standard topics including holomorphic maps, morphisms, derivatives, tangent bundles, product manifolds and submanifolds are presented. Although this framework is elementary, it lays the necessary foundation for all subsequent developments.展开更多
In this paper, we are concerned with the classification of operators on complex separable Hilbert spaces, in the unitary equivalence sense and the similarity sense, respectively. We show that two strongly irreducible ...In this paper, we are concerned with the classification of operators on complex separable Hilbert spaces, in the unitary equivalence sense and the similarity sense, respectively. We show that two strongly irreducible operators A and B are unitary equivalent if and only if W＊（A＋B）′≈M2（C）, and two operators A and B in B1（Ω） are similar if and only if A′（AGB）/J≈M2（C）. Moreover, we obtain V（H^∞（Ω,μ）≈N and Ko（H^∞（Ω,μ）≈Z by the technique of complex geometry, where Ω is a bounded connected open set in C, and μ is a completely non-reducing measure on Ω.展开更多
基金This paper is a talk on the held in Nanjing, P. R. China, July, 2004.
文摘Based on locally compact perturbations of the identity map similar to the Fredholm structures on real Banach manifolds, complex manifolds with inverse mapping theorem as part of the defintion are proposed. Standard topics including holomorphic maps, morphisms, derivatives, tangent bundles, product manifolds and submanifolds are presented. Although this framework is elementary, it lays the necessary foundation for all subsequent developments.
基金the 973 Project of China and the National Natural Science Foundation of China(Grant No.19631070)
文摘In this paper, we are concerned with the classification of operators on complex separable Hilbert spaces, in the unitary equivalence sense and the similarity sense, respectively. We show that two strongly irreducible operators A and B are unitary equivalent if and only if W＊（A＋B）′≈M2（C）, and two operators A and B in B1（Ω） are similar if and only if A′（AGB）/J≈M2（C）. Moreover, we obtain V（H^∞（Ω,μ）≈N and Ko（H^∞（Ω,μ）≈Z by the technique of complex geometry, where Ω is a bounded connected open set in C, and μ is a completely non-reducing measure on Ω.
