# Answer on Functional Analysis Question for sima

Question #38327

if T belongs to b(X,Y) is not compact can the restriction of T to an infinite dimensional subspace of X be compact?

Expert's answer

Yes. Look at the following example. Take any infinite dimensional Banach spaces X and Y. Let S∈K(X), then restriction of T:=S⊕∞1Y∈B(X⊕∞Y) to X is S which is compact by construction.

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