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arXiv · 2505.16111

Two tuples of noncommutative Orlicz sequence spaces and some geometry properties

Ma Zhenhua·Jiang Lining
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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.

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Ma Zhenhua, Jiang Lining. 2025-05-22. Two tuples of noncommutative Orlicz sequence spaces and some geometry properties. https://arxiv.org/abs/2505.16111

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