Rank of positive matrix measures
Roderic Murufas · Pacific Journal of Mathematics · 1983
RODERIC MURUFASLet L be a selfadjoint operator in a separable Hilbert space.Here we define a concept of rank for positive matrix measures from which the spectral multiplicity of a point in the spectrum of L may be determined.In the process, a diagonalization procedure for positive matrix measures is constructed, connecting the concept of a spectral matrix to the abstract measures of a spectral representation.The definitions and theorems appearing in paragraph 1-6 are taken directly from the article of Rosenberg [3].They establish background material essential to the article and serve to familiarize the reader with typical manipulations of positive matrix measures.