Antisymmetric relations of operators which satisfy specified conditions

Abstract

This paper is provided a condition that two relations $\bigtriangleup $ and $\square$ are equivalent.
It is shown that if $T\square S$, then $(TS^\dag)^\dag \bigtriangleup TS^\dag$ and $(S^\dag T)^\dag \bigtriangleup S^\dag T$.
Also, it is presented a condition that $T^\dag \bigtriangleup T$ establishes.