Invariants of the block tensor product (Q1320007)

The authors consider the following problem: Let \(X_ i\), \(i=1,2\), be vector spaces over \(\mathbb{C};Y_ i\) subspaces of \(X_ i\), \(i=1,2\): and \(f_ i\): \(Y_ i\to X_ i\), \(i=1,2\), linear maps defined on a subspace. They characterize the invariant of block similarity of \(f_ 1\otimes f_ 2\): \(Y_ 1\otimes Y_ 2\to X_ 1\otimes X_ 2\) in terms of the block similarity invariants of \(f_ 1\) and \(f_ 2\). The paper contains sections on Brunowsky numbers of the block direct product and elementary divisors of the block direct product.