Full Subcategory: Hilb ⊊ Ban_k

Hilb is a full subcategory of Ban_k. When any two Banach spaces over fields k of Ban_k are Hilbert spaces in Hilb, all short linear maps between them are short linear maps in Hilb too. Put another way, Hilb has only some of the objects of Ban_k, but all of the arrows.

In terms of stuff, structure, and properties, Hilbert spaces are like Banach spaces over fields k but with extra properties.

full_subcategories: Hilb, Ban_k

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