Geometric Interpolation in n-Tuples of Noncommutative $L_p$-Spaces

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发表日期：

2024年4月30日

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Feng Zhang

摘要

Let $\mathcal {M}$ $M$ be a von Neumann algebra with a normal faithful semifinite trace. In this paper, we consider that in n-tuples of noncommutative $L_p$ $L_{p}$ -spaces $l_s^{(n)}(L_p(\mathcal {M}))$ $l_{s}^{(n)} (L_{p} (M))$ , the norm is invariant under the action of invertible elements in $\mathcal {M}$ $M$ . Then we prove that the complex interpolating theorem in the case of $l_s^{(n)}(L_p(\mathcal {M}))$ $l_{s}^{(n)} (L_{p} (M))$ . Using this result, we obtain that Clarkson’s inequalities for n-tuples of operators with weighted norm of noncommutative $L_p$ $L_{p}$ -spaces, where the weight being a positive invertible operator in $\mathcal {M}$ $M$ .

Geometric Interpolation in n-Tuples of Noncommutative \(L_p\)-Spaces

摘要