Applications of Michael’s continuous selection theorem to operator extension problems

Zippin, M.

doi:10.1090/S0002-9939-99-04777-2

Applications of Michael’s continuous selection theorem to operator extension problems
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Proc. Amer. Math. Soc. 127 (1999), 1371-1378 Request permission

Abstract:

A global approach and Michael’s continuous selection theorem are used to prove a slightly improved version of the Lindenstrauss - Pełczyński extension theorem for operators from subspaces of $c_0$ into $C (K)$ spaces.

References

W. B. Johnson and M. Zippin, Extension of operators from subspaces of $c_0(\Gamma )$ into $C(K)$ spaces, Proc. Amer. Math. Soc. 107 (1989), no. 3, 751–754. MR 984799, DOI 10.1090/S0002-9939-1989-0984799-7
J. Lindenstrauss and A. Pełczyński, Contributions to the theory of the classical Banach spaces, J. Functional Analysis 8 (1971), 225–249. MR 0291772, DOI 10.1016/0022-1236(71)90011-5
Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. I, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 92, Springer-Verlag, Berlin-New York, 1977. Sequence spaces. MR 0500056, DOI 10.1007/978-3-642-66557-8
Saunders MacLane, Steinitz field towers for modular fields, Trans. Amer. Math. Soc. 46 (1939), 23–45. MR 17, DOI 10.1090/S0002-9947-1939-0000017-3
M. Zippin, A global approach to certain operator extension problems, Functional analysis (Austin, TX, 1987/1989) Lecture Notes in Math., vol. 1470, Springer, Berlin, 1991, pp. 78–84. MR 1126740, DOI 10.1007/BFb0090215