The vector space Hom(V,W) remains the same if either the domain norm or the range norm is replaced by an equivalent norm.(adsbygoogle = window.adsbygoogle || []).push({});

Does 'remain the same' here means that the bound of every mapping in Hom(V,W) is unchanged?

How come the above theorem can be considered as a corollary of the following theorem?

If U, V and W are normed linear spaces, and if T is in Hom(U,V) and S is in Hom(V,W), then ST is in Hom(U,W) and || ST || <= ||S|| ||T||

Thanks

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# Equivalent norms

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