Given two quantum system $A$ and $B$, their Hilbert space $H_{A}$ and $H_{B}$, we can form a tensor product $H_{A}\otimes H_{B}$ to describe the larger system $A$ with $B$. Of course the operators act on $H_{A}$ and $H_{B}$ have to be tensor product as well. Assume all quantum observables are bounded(which is not true, but my focus is not here). We denote the space of bounded linear operator act on $H_{A}\otimes H_{B}$ be $L(H_{A}\otimes H_{B})$, then $L(H_{A}\otimes H_{B})$ is a Banach space with some norm. As far as I know, the choice of norm for tensor product of norm space is not unique. Are all these norms physically equivalent?
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