# Answer to Question #38327 in Functional Analysis 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.

Need a fast expert's response?

Submit orderand get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

## Comments

## Leave a comment