Let X be a normed linear space and let Y be a Banach space. Let Then...

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Let X be a normed linear space and let Y be a Banach space. Let Then with the norm || A|| that B(X,Y) is a Banach B(X,Y)= {A|A: X → Y is a bounded linear operator}. sup||||1||Ar||, B(X,Y) is a normed linear space (you need not show this). Prove space; that is, prove that B(X,Y) is complete. = Let X be a normed linear space and let Y be a Banach space. Let Then with the norm || A|| that B(X,Y) is a Banach B(X,Y)= {A|A: X → Y is a bounded linear operator}. sup||||1||Ar||, B(X,Y) is a normed linear space (you need not show this). Prove space; that is, prove that B(X,Y) is complete. =

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