AN UPPER BOUND ON THE DIMENSION OF THE REFLEXIVITY CLOSURE

作者：Ambrozie Calin^*; Kuzma Bojan; Muller Vladimir

来源：Proceedings of the American Mathematical Society, 2010, 138(5): 1721-1731.

• Determinantal varieties
• space of linear operators
• intersection of images
• reflexivity defect

Let V, W be linear spaces over an algebraically dosed field, and let S be an it dimensional subspace of linear operators that maps V into W. We give a sharp upper bound for the dimension of the intersection of all images of nonzero operators from S, namely dim (boolean AND(A is an element of S\{0}) ImA) <= dim V - n + 1. As an application, we also give a sharp upper bound for the dimension of the reflexivity closure Ref S of S, namely dim (Ref S) <= n(n + 1)/2.

• 出版日期2010-5