In this work, we study a comparison of norms in non-commutative spaces of \(\tau \) -measurable operators associated with a semifinite von Neumann algebra. In particular, we obtain Nazarov–Podkorytov type lemma Nazarov et al. (Complex analysis, operators, and related topics. Operatory theory: advances, vol 113, pp 247–267, 2000) and extend the main results in Astashkin et al. (Math Ann, 2023. https://doi.org/10.1007/s00208-023-02606-w) to non-commutative settings. Moreover, we complete the range of the parameter p for \(0<p<1.\)
