Upper triangular Toeplitz matrices and real parts of quasinilpotent operators Academic Article uri icon


  • We show that every self-adjoint matrix B of trace 0 can be realized as B = T + T* for a nilpotent matrix T with T KB, for a constant K that is independent of matrix size. More particularly, if D is a diagonal, self-adjoint nn matrix of trace 0, then there is a unitary matrix V = XUn, where X is an n n permutation matrix and Un is the n n Fourier matrix, such that the upper triangular part, T, of the conjugate V*DV of D satisfies T KD. This matrix T is a strictly upper triangular Toeplitz matrix such that T + T* = V*DV. We apply this and related results to give partial answers to questions about real parts of quasinilpotent elements in finite von Neumann algebras. Indiana University Mathematics Journal.

published proceedings

  • Indiana University Mathematics Journal

author list (cited authors)

  • Dykema, K., Fang, J., & Skripka, A.

citation count

  • 1

complete list of authors

  • Dykema, Ken||Fang, Junsheng||Skripka, Anna

publication date

  • January 2014