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 $\bigoplus\limits_{j=1}^{2}S_{\varphi_{j},p}$, where $S_{\varphi_{j}}$ denotes a noncommutative Orlicz sequence space. By leveraging the three-line theorem, we establish the Riesz-Thorin interpolation theorem for $\bigoplus\limits_{j=1}^{2}S_{\varphi_{j},p}$. As applications, we derive bound for the nonsquare and von Neumann-Jordan constant of noncommutative Orlicz space $S_{\varphi_{s}} (0<s\leq1)$, where $\varphi_{s}$ is an intermediate function.