Question: Let ( X , ) be a Banach space. Consider the closed disjoint subspaces Y and Z. Show that Y Z is closed in X

Let (X,) be a Banach space. Consider the closed disjoint subspaces Y and Z. Show that YZ is closed in X if and only if there is a c>0 in R (real) for any y in Y, z in Z such that c[y+z]y+z .

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