Extension of operators from subspaces of c 0 ( ) c_ 0(Gamma ) into C ( K ) C(K) spaces Academic Article

It is shown that for every > 0 varepsilon > 0 , every bounded linear operator T T from a subspace X X of c 0 ( ) {c_0}left ( Gamma
ight ) into a C ( K ) Cleft ( K
ight ) space has an extension T {mathbf {T}} from c 0 ( ) {c_0}left ( Gamma
ight ) into the C ( K ) Cleft ( K
ight ) space such that T ( 1 + ) T left | {mathbf {T}}
ight | leq left ( {1 + varepsilon }
ight )left | T
ight | . Even when Gamma is countable, T T is compact, and X X