I'm not sure how to show that the set of all bounded multilinear maps is a vector space. Could someone help me?
2026-03-28 13:27:18.1774704438
The set of all bounded multilinear maps
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Hint: First, you want to show that the $0$ map is bounded and multilinear.
Then, you need to demonstrate that if $f,g$ are bounded multilinear maps, and $\alpha$ is an element of your original field, then $\alpha f + g$ is also a bounded multilinear map.