TY - JOUR
T1 - Extension of operators from subspaces of c0(Γ)into C(K) spaces
AU - Johnson, W. B.
AU - Zippin, M.
PY - 1989/11
Y1 - 1989/11
N2 - It is shown that for every ε> 0, every bounded linear operator T from a subspace X of C0(Γ) into a C(K) space has an extension T from C0(Γ) into the C(K) space such that ||T|| ≤ (1 + ε)||T||. Even when Γis countable, T is compact, and X has codimension 1 in Cq, the “ε” cannot be replaced by 0. These results answer questions raised by J. Lindenstrauss and A. Pelczynski in 1971.
AB - It is shown that for every ε> 0, every bounded linear operator T from a subspace X of C0(Γ) into a C(K) space has an extension T from C0(Γ) into the C(K) space such that ||T|| ≤ (1 + ε)||T||. Even when Γis countable, T is compact, and X has codimension 1 in Cq, the “ε” cannot be replaced by 0. These results answer questions raised by J. Lindenstrauss and A. Pelczynski in 1971.
KW - Continuous selections
KW - Extension of operators
KW - Hahn-Banach extensions
KW - Operators into C(K)
UR - http://www.scopus.com/inward/record.url?scp=84966209124&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-1989-0984799-7
DO - 10.1090/S0002-9939-1989-0984799-7
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AN - SCOPUS:84966209124
SN - 0002-9939
VL - 107
SP - 751
EP - 754
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 3
ER -