Fuglede-type decompositions of representations
Volume 151 / 2002
Studia Mathematica 151 (2002), 87-98
MSC: Primary 47A60; Secondary 47A15, 46J10, 46J25.
DOI: 10.4064/sm151-1-6
Abstract
It is shown that reducing bands of measures yield decompositions not only of an operator representation itself, but also of its commutant. This has many consequences for commuting Hilbert space representations and for commuting operators on Hilbert spaces. Among other things, it enables one to construct a Lebesgue-type decomposition of several commuting contractions without assuming any von Neumann-type inequality.
