|1Ashurova, EN, 2Ostrovskyi, VL, 2Samoilenko, Yu.S |
1Chiltern Clinical Research in Ukraine, Kyiv
2Institute of Mathematics of the NAS of Ukraine, Kyiv
|Dopov. Nac. akad. nauk Ukr. 2017, 10:3-9|
We study properties of representations of the involutive algebra generated by self-adjoint idempotents, q1, . . ., qn and p1, . . ., pm, which satisfy the conditions q1 + . . . + qn = e, pjpk = 0, j ≠ k. The corresponding collections of projections in a Hilbert space arise in the study of the Fredholm properties of Toeplitz operators. In particular, for generic irredu cible representations with dim Pj = 1, j = 1 . . . , m, we have constructed a commuting family of normal operators, whose joint spectrum determines the representation up to unitary equivalence.
|Keywords: families of orthoprojections, Toeplitz operators|
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