n-Reflexivity of Subspaces of Operators
by
Zhidong Pan
Saginaw Valley State University
Coauthors: Jiankui Li(Univ of New Hampshire)

Let B(H) be the set of bounded operators on a Hilbert space H and S be a finite dimensional subspace of B(H). Define the local dimension of S, denoted k(S), as follows, k(S)=max{dim[Sx]: x in H}. We will discuss some basic properties of k(S), which we use to show that if k is the local dimension of S then S is k-reflexive. As an application of the above, we prove that if dim(S)=n then S is [\surd{2n}]-reflexive, where [t] denotes the integer part of a positive number t.

Date received: April 30, 1999