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Ma Zhenhua

Publications and source records attributed to Ma Zhenhua.

4 recordsLinked to original sources
arXiv2025

Two tuples of noncommutative Orlicz sequence spaces and some geometry properties

The primary contribution of this study lies in proposing a new concept termed $2$-tuples of noncommutative Orlicz sequence spaces $\bigoplus\limits_{j=1}^{2}S_{φ_{j},p}$, where $S_{φ_{j}}$ denotes a noncommutative Orlicz sequence space. By leveraging the three-line theorem, we establish the Riesz-Thorin interpolation theorem for $\bigoplus\limits_{j=1}^{2}S_{φ_{j},p}$. As applications, we derive bound for the nonsquare and von Neumann-Jordan constant of noncommutative Orlicz space $S_{φ_{s}} (0<s\leq1)$, where $φ_{s}$ is an intermediate function.

math.FA↗
arXiv2021

N-tuple wights noncommutative Orlicz spaces and some geometrical properties

This paper studies the $N$-tuple noncommutative Orlicz spaces $\bigoplus\limits_{j=1}^{n}L_{p,λ}^{(Φ_{j})}(\widetilde{\mathcal{M}},τ)$, where $L^{(Φ_{j})}(\widetilde{\mathcal{M}},τ)$ is noncommutative Orlicz spaces and $\widetilde{\mathcal{M}}$ is the $τ$-measurable operators. Based on the maximum principle, we give the Riesz-Thorin interpolation theorem on $\bigoplus\limits_{j=1}^{n}L_{p,λ}^{(Φ_{j})}(\widetilde{\mathcal{M}},τ)$ . As applications, the Clarkson inequality and some geometrical properties such as uniform convexity and unform smooth of noncommutative Orlicz space.

math.OA↗
arXiv2019

Compact operators under Orlicz functions

In this paper, the definition of noncommutative Orlicz sequence spaces is given, these spaces generalize the Schatten classes Sp(H). After some relations of trace and norm on this spaces have been researched, one give the criterion of reflexivity of these spaces. At last, as an application, we find the Toeplitz operator on the Bergman space belongs to some noncommutative Orlicz sequence spaces, hence the trace and the norm of operator could be computed.

math.FA↗