Ghosh, SagarSagarGhoshMisra, GadadharGadadharMisra2025-08-282025-08-282023-04-01https://arxiv.org/abs/2304.08021http://repository.iitgn.ac.in/handle/IITG2025/20146In this semi-expository short note, we prove that the only homogeneous \textit{pure} hyponormal operator T with rank(T?T?TT?)=1, modulo unitary equivalence, is the unilateral shift.en-USM�bius invariantPincusHilbert spaceOrthonormal basisPutnam's inequalitye-Print123456789/555