Two tuples of noncommutative Orlicz sequence spaces and some geometry properties

Abstract

The primary contribution of this study lies in proposing a new concept termed $2$-tuples of noncommutative Orlicz sequence spaces $\underset{j=1}{\overset{2}{⨁}}{S}_{{\phi }_j,p}$, where $S_{{\phi }_j}$ denotes a noncommutative Orlicz sequence space. By leveraging the three-line theorem, we establish the Riesz-Thorin interpolation theorem for $\underset{j=1}{\overset{2}{⨁}}{S}_{{\phi }_j,p}$. As applications, we derive bound for the nonsquare and von Neumann-Jordan constant of noncommutative Orlicz space $S_{{\phi }_s}(0<s\le 1)$, where ${\phi }_s$ is an intermediate function.