Topological properties of the block numerical range of operator matrices
Agnes Radl, Manfred P. H. Wolff · Operators and Matrices · 2020
We show that the block numerical range of an nn -operator matrix A corresponding to an operator A on the Banach space X with respect to a decomposition X = X j has at most n connected components. We then characterize operator matrices with finite block numerical range. As an important tool we prove an inclusion theorem for the block numerical ranges of the principal submatrices of A .