When products of selfadjoints are normal

Albrecht, E.; Spain, P.

doi:10.1090/S0002-9939-00-05830-5

When products of selfadjoints are normal
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by E. Albrecht and P. G. Spain PDF

Proc. Amer. Math. Soc. 128 (2000), 2509-2511 Request permission

Abstract:

Suppose that $h, k \in \mathcal {L}(\mathcal {H})$ are two selfadjoint bounded operators on a Hilbert space $\mathcal {H}$. It is elementary to show that $hk$ is selfadjoint precisely when $hk = kh$. We answer the following question: Under what circumstances must $hk$ be selfadjoint given that it is normal?

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