The Spectral Theory of Upper Triangular Matrices with Entries in a Banach Algebra
Bruce Alan Barnes · Mathematische Nachrichten · 2002
Assume that T is an upper triangular square matrix with entries in a unital Banach algebra. The main question studied here is: Under what conditions on the entries in T is it true that the spectrum of T is the union of the spectra of the diagonal entries of T? Also some results are proved concerning the Fredholm theroy of matrices with operator entries.