Tusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3120180101Operators with compatible ranges in an algebra generated by two orthogonal projections1171224516610.22034/aot.1702-1111ENIlya MSpitkovskyNYUADJournal Article20170202The 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.http://www.aot-math.org/article_45166_aed3194d347d41e51b89267a4029d5d6.pdf