Abstract
LetA andB be positive invertible operators. Then for eachp≥0 andr≥0, two inequalities
are equivalent. In this paper, we shall show relations between these inequalities in caseA andB are not invertible. And we shall show some applications of this result to operator classes.
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Ito, M., Yamazaki, T. Relations between two inequalities\((B^{\tfrac{r}{2}} A^p B^{\tfrac{r}{2}} )^{\tfrac{r}{{p + r}}} \geqslant B^r andA^p \geqslant (A^{\tfrac{p}{2}} B^r A^{\tfrac{p}{2}} )^{\tfrac{p}{{p + r}}}\) and their applications. Integr equ oper theory 44, 442–450 (2002). https://doi.org/10.1007/BF01193670
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DOI: https://doi.org/10.1007/BF01193670