Unitary Automorphisms of the Space of (T+H)-Matrices of Order Four

摘要

Matrices U in unitary group U_4 that satisfy the implication anyA ∈ TH_4 → B = U~*AU ∈ TH_4 are examined. Here, TH_4 is a set of order four (T+H )-matrices. Such matrices U can be identified with unitary automorphisms of the space TH_4. Our problem is whether the boundary of U can be free of zeros. (The boundary of a matrix is the collection of its entries in the first and last row and the first and last column.) It is shown that matrices U with an entirely nonzero boundary do exist, in contrast to the situation for the unitary automorphisms of the spaces of order four Toeplitz and Hankel matrices.