Reflexivity of Tensor Products of Linear Transformations

Abstract

Abstract. Let A and B be linear transformations on finite-dimensional Hubert space. We characterize the reflexivity of A ® B in terms of certain characteristics of A and B .

On Rank Two Linear Transformations and Reflexivity

“…For example, the singleton sequence 5 can be lengthened to the reflexive sequences 5,4; 5,5; and 5,6. On the other hand, the only two-term reflexive extension of the Jordan sequence (5,7) is (5,7), (5,7). Even the three-term reflexive extensions of (5, 7) are limited.…”

“…In Proposition 6.4, we showed that the tensor product of two nilpotent operators is always reflexive. As discussed in [7], the situation is much more complicated when the hypothesis of nilpotence is dropped. From the point of view of Theorem 7.4, the problem arises from the failure of idempotents in stf(a®b) corresponding to points in a(a (x) b) to be simple tensor products of idempotents in s/(a) and sJ(b).…”