Operators with compatible ranges in an algebra generated by two orthogonal projections

Document Type: Article dedicated to Uffe Haagerup

Author

NYUAD

Abstract

The criterion is obtained for operators A from the algebra generated by two orthogonal projections P,Q to have a compatible range, i.e., coincide with the hermitian conjugate of A on the orthogonal complement to the sum of their kernels. In the particular case of A being a polynomial in P,Q, some easily verifiable conditions are derived.

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