Central maps that are Lorentz-entanglement breaking or annihilating are exactly those whose underlying operator has 2-dominated norm gamma_2* <= lambda or 2-summing norm pi_2 <= lambda; an explicit non-entanglement-breaking Lorentz-entanglement-breaking map on M3(C)+ is constructed.
Limit formulas for norms of tensor power operators
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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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Annihilating and breaking Lorentz cone entanglement
Central maps that are Lorentz-entanglement breaking or annihilating are exactly those whose underlying operator has 2-dominated norm gamma_2* <= lambda or 2-summing norm pi_2 <= lambda; an explicit non-entanglement-breaking Lorentz-entanglement-breaking map on M3(C)+ is constructed.