Geodesic
Unitarizable and non-unitarizable represenations of algebras generated by idempotents
Algebra and discrete mathematics, no. 3 (2004), pp. 111-125.

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The problem of unitarization of representations of algebras generated by idempotents with linear relations is studied. Construction of non-unitarizable representations for some sub-intervals of continuous spectrum is presented. Unitarization of representations from discrete series is proven.
Keywords: idempotent, projection, representation, unitarization, Hilbert space. 
@article{ADM_2004_3_a8,
     author = {Stanislav Popovych and Lyudmila Turowska},
     title = {Unitarizable and non-unitarizable represenations of algebras generated by idempotents},
     journal = {Algebra and discrete mathematics},
     pages = {111--125},
     publisher = {mathdoc},
     number = {3},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2004_3_a8/}
}
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Stanislav Popovych; Lyudmila Turowska. Unitarizable and non-unitarizable represenations of algebras generated by idempotents. Algebra and discrete mathematics, no. 3 (2004), pp. 111-125. http://geodesic.mathdoc.fr/item/ADM_2004_3_a8/