Extensions by spaces of continuous functions
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- by Jesús M. F. Castillo and Yolanda Moreno PDF
- Proc. Amer. Math. Soc. 136 (2008), 2417-2423 Request permission
Abstract:
We present two complementary results on the splitting of exact sequences having the form $0\to C(K) \to E \to X\to 0$. The first one characterizes the Banach spaces $X$ such that $\operatorname {Ext}(X, C(K))=0$ for every compact space $K$. The second is a nonlinear generalization of Zippin’s criterion for the extension of $C(K)$-valued operators.References
- Félix Cabello Sánchez and Jesús M. F. Castillo, Duality and twisted sums of Banach spaces, J. Funct. Anal. 175 (2000), no. 1, 1–16. MR 1774849, DOI 10.1006/jfan.2000.3598
- F. Cabello Sánchez, J. M. F. Castillo, N. J. Kalton, and D. T. Yost, Twisted sums with $C(K)$ spaces, Trans. Amer. Math. Soc. 355 (2003), no. 11, 4523–4541. MR 1990760, DOI 10.1090/S0002-9947-03-03152-0
- Félix Cabello Sánchez, Jesús M. F. Castillo, and Fernando Sánchez, Nonlinear metric projections in twisted twilight, Rev. R. Acad. Cienc. Exactas Fís. Nat. (Esp.) 94 (2000), no. 4, 473–483. Perspectives in mathematical analysis (Spanish). MR 1865749
- Jesús M. F. Castillo and Manuel González, Three-space problems in Banach space theory, Lecture Notes in Mathematics, vol. 1667, Springer-Verlag, Berlin, 1997. MR 1482801, DOI 10.1007/BFb0112511
- W. B. Johnson and M. Zippin, Extension of operators from weak$^*$-closed subspaces of $l_1$ into $C(K)$ spaces, Studia Math. 117 (1995), no. 1, 43–55. MR 1367692
- N. J. Kalton, The three space problem for locally bounded $F$-spaces, Compositio Math. 37 (1978), no. 3, 243–276. MR 511744
- N. J. Kalton, On subspaces of $c_0$ and extension of operators into $C(K)$-spaces, Q. J. Math. 52 (2001), no. 3, 313–328. MR 1865904, DOI 10.1093/qjmath/52.3.313
- N. J. Kalton and N. T. Peck, Twisted sums of sequence spaces and the three space problem, Trans. Amer. Math. Soc. 255 (1979), 1–30. MR 542869, DOI 10.1090/S0002-9947-1979-0542869-X
- N. J. Kalton and A. Pełczyński, Kernels of surjections from $\scr L_1$-spaces with an application to Sidon sets, Math. Ann. 309 (1997), no. 1, 135–158. MR 1467651, DOI 10.1007/s002080050107
- M. Zippin, The embedding of Banach spaces into spaces with structure, Illinois J. Math. 34 (1990), no. 3, 586–606. MR 1053564
Additional Information
- Jesús M. F. Castillo
- Affiliation: Departamento de Matemáticas, Universidad de Extremadura, Avenida de Elvas, 06071 Badajoz, Spain
- MR Author ID: 247518
- ORCID: 0000-0003-3032-966X
- Email: castillo@unex.es
- Yolanda Moreno
- Affiliation: Departamento de Matemáticas, Universidad de Extremadura, Avenida de Elvas, 06071 Badajoz, Spain
- Email: ymoreno@unex.es
- Received by editor(s): May 5, 2004
- Published electronically: March 4, 2008
- Additional Notes: This work was supported in part by MTM2004-02635.
- Communicated by: Jonathan M. Borwein
- © Copyright 2008 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 136 (2008), 2417-2423
- MSC (2000): Primary 46M18, 46B20
- DOI: https://doi.org/10.1090/S0002-9939-08-08820-5
- MathSciNet review: 2390508