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↗