Abstract. We reprove a recent result of Z. Sebestyén and Zs. Tarcsay [9]: If $T^*T$ and $TT^*$ are self-adjoint, then $T$ is closed.

DOI: 10.14232/actasm-018-295-y

AMS Subject Classification (1991): 47B25; 47B65

Keyword(s): von Neumann's theorem

Received May 10, 2018. (Registered under 45/2018.)