# Extension of compact operator

Let XX and ZZ be two Banach spaces and YY be a closed subspace of XX. Let T:Y→ZT\colon Y \rightarrow Z be a compact operator. Does there exist a compact operator ˜T:X→Z\tilde{T}\colon X\rightarrow Z such that ˜T⏐Y=T\tilde{T}\arrowvert Y=T?

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