Unitary equivalence and decompositions of finite systems of closed densely defined operators in Hilbert spaces
Piotr Niemiec
GDML_Books, (2012), p.

An ideal of N-tuples of operators is a class invariant with respect to unitary equivalence which contains direct sums of arbitrary collections of its members as well as their (reduced) parts. New decomposition theorems (with respect to ideals) for N-tuples of closed densely defined linear operators acting in a common (arbitrary) Hilbert space are presented. Algebraic and order (with respect to containment) properties of the class CDDN of all unitary equivalence classes of such N-tuples are established and certain ideals in CDDN are distinguished. It is proved that infinite operations in CDDN may be reconstructed from the direct sum operation of a pair. Prime decomposition in CDDN is proposed and its uniqueness (in a certain sense) is established. The issue of classification of ideals in CDDN (up to isomorphism) is discussed. A model for CDDN is described and its concrete realization is presented. A new partial order of N-tuples of operators is introduced and its fundamental properties are established. The importance of unitary disjointness of N-tuples and the way how it ’tidies up’ the structure of CDDN are emphasized.

EUDML-ID : urn:eudml:doc:286018
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     author = {Piotr Niemiec},
     title = {Unitary equivalence and decompositions of finite systems of closed densely defined operators in Hilbert spaces},
     series = {GDML\_Books},
     year = {2012},
     zbl = {1256.47007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm482-0-1}
}
Piotr Niemiec. Unitary equivalence and decompositions of finite systems of closed densely defined operators in Hilbert spaces. GDML_Books (2012),  http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm482-0-1/