Unitarizable and non-unitarizable represenations of algebras generated by idempotents

Stanislav Popovych^a, Lyudmila Turowska<sup>b

a</sup> Department of Mechanics and Mathematics, Kyiv Taras Shevchenko University, 01033 Kyiv, Ukraine
^b Chalmers Tekniska Högskola, Matematiska Vetenskaper, SE 412 96, Göteborg, Sweden

Abstract: 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.

MSC: 16W10, 47L30, 16G20

Language: English

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