Extension of operators from subspaces of c0(Γ)into C(K) spaces

W. B. Johnson; M. Zippin

doi:10.1090/S0002-9939-1989-0984799-7

Extension of operators from subspaces of c₀(Γ)into C(K) spaces

W. B. Johnson
, M. Zippin

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	751-754
Number of pages	4
Journal	Proceedings of the American Mathematical Society
Volume	107
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-1989-0984799-7
State	Published - Nov 1989

Keywords

Continuous selections
Extension of operators
Hahn-Banach extensions
Operators into C(K)

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10.1090/S0002-9939-1989-0984799-7

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abstract = "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.",

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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)

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Extension of operators from subspaces of c₀(Γ)into C(K) spaces

Abstract

Keywords

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