Piotr Niemiec
Published 2013-08-12Version 1
It is shown that each linear operator on a separable Hilbert space which generates a finite type I von Neumann algebra has, up to unitary equivalence, a unique representation as a direct integral of inflations of mutually unitary inequivalent irreducible matrices. This leads to a simplification of the so-called prime (or central) decomposition and the multiplicity theory for such operators. The concept of so-called p-isomorphisms between special classes of such operators is discussed. All results are formulated in more general settings; that is, for tuples of closed densely defined operators affiliated with finite type I von Neumann algebras.
Direct integrals of strongly irreducible operators
Orthogonal $\ell_1$-sets and extreme non-Arens regularity of preduals of von Neumann algebras
On the measure of the spectrum of direct integrals
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