On representations of the algebras generated by a finite resolution of the identity and a collection of jointly orthogonal projections
DOI:
https://doi.org/10.15407/dopovidi2017.10.003Keywords:
families of orthoprojections, Toeplitz operatorsAbstract
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.
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