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arXiv · 1308.2510

Direct integrals of matrices

Piotr Niemiec
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Abstract

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.

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Piotr Niemiec. 2013-08-12. Direct integrals of matrices. https://doi.org/10.1007/s11856-016-1298-5

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