Question: The space BL(X, Y) of all bounded linear functions from X to Y is a normed linear space, with norm It is a Banach space

The space BL(X, Y) of all bounded linear functions from X to Y is a normed linear space, with norm

It is a Banach space (complete normed linear space) if Y is complete. The following proposition is an important result regarding bounded linear functions.

f|| = sup{ ||f(x)|| || = 1}

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