Related papers: Limit formulas for norms of tensor power operators

Limit formulas for norms of tensor power operators

URL: http://arxiv.org/abs/2410.23063v1
Date: Wed, 30 Oct 2024 14:39:21 GMT
Title: Limit formulas for norms of tensor power operators
Authors: Guillaume Aubrun, Alexander Müller-Hermes,
Abstract summary: Given an operator $phi:Xrightarrow Y$ between Banach spaces, we consider its tensor powers. We show that after taking the $k$th root, the operator norm of $phiotimes k$ converges to the $2$-dominated norm.
Score: 49.1574468325115
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Abstract: Given an operator $\phi:X\rightarrow Y$ between Banach spaces, we consider its tensor powers $\phi^{\otimes k}$ as operators from the $k$-fold injective tensor product of $X$ to the $k$-fold projective tensor product of $Y$. We show that after taking the $k$th root, the operator norm of $\phi^{\otimes k}$ converges to the $2$-dominated norm $\gamma^*_2(\phi)$, one of the standard operator ideal norms.

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