2020/02/04 by Sebestyén, Zoltán, Tarcsay, Zsigmond
#47A5 #47B25 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2002.01213
We provide necessary and sufficient conditions for a pair S,T of Hilbert space operators in order that they satisfy S^*=T and T^*=S. As a main result we establish an improvement of von Neumann's classical theorem on the positive self-adjointness of S^*S for two variables. We also give some new characterizations of self-adjointness and skew-adjointness of operators, not requiring their symmetry or skew-symmetry, respectively.