Rank of positive matrix measures

Roderic Murufas

Vol. 108 (1983), No. 1, 177–190

DOI: 10.2140/pjm.1983.108.177

Abstract

Let 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.

Mathematical Subject Classification 2000

Primary: 47B15

Secondary: 28B05

Milestones

Received: 28 January 1982

Revised: 7 June 1982

Published: 1 September 1983