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0.1 Norms of Linear application[2CM]
In the following \((X,\| \| _ X)\)and \((Y,\| \| _ Y)\) will be normed spaces; \(A:X→ Y\) is a linear application; we define the induced norm as
\[ \| A\| _{X,Y}{\stackrel{.}{=}}\sup _{x∈ X~ ,~ \| x\| _ X≤ 1} \| Ax\| _ Y~ . \]
Exercises
[11B]
[11C]
[11D]
[11F]
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