Hyperreflexivity constants of some spaces of matrices

Text of abstract For some reflexive spaces of matrices we calculate or estimate hyperreflexivity constants with respect to different operator norms on the space of matrices. It is known that the hyperreflexivity constant of every one-dimensional space of operators on a Hilbert space is 1. We show that for Banach spaces this does not hold in general. Namely, if 2×2 matrices are considered as operators on , then the hyperreflexivity constant of the one-dimensional subspace which is spanned by the identity matrix is .