On subprojectivity of 𝐶(𝐾,𝑋)

González, Manuel; Pello, Javier

doi:10.1090/proc/14481

On subprojectivity of $C(K,X)$
HTML articles powered by AMS MathViewer

by Manuel González and Javier Pello PDF

Proc. Amer. Math. Soc. 147 (2019), 3425-3429 Request permission

Abstract:

We show that the Banach space $C(K,X)$ is subprojective if $K$ is scattered and $X$ is subprojective.

References

Fernando Albiac and Nigel J. Kalton, Topics in Banach space theory, Graduate Texts in Mathematics, vol. 233, Springer, New York, 2006. MR 2192298
M. Eidelheit, Concerning rings of continuous functions, Ann. of Math. (2) 41 (1940), 391–393. MR 1449, DOI 10.2307/1969012
Elói M. Galego, Manuel González, and Javier Pello, On subprojectivity and superprojectivity of Banach spaces, Results Math. 71 (2017), no. 3-4, 1191–1205. MR 3648469, DOI 10.1007/s00025-016-0558-3
Elói Medina Galego and Christian Samuel, The subprojectivity of the projective tensor product of two $C(K)$ spaces with $|K|=\aleph _0$, Proc. Amer. Math. Soc. 144 (2016), no. 6, 2611–2617. MR 3477078, DOI 10.1090/proc/12926
Manuel González, The perturbation classes problem in Fredholm theory, J. Funct. Anal. 200 (2003), no. 1, 65–70. MR 1974088, DOI 10.1016/S0022-1236(02)00071-X
Manuel González, Antonio Martínez-Abejón, and Margot Salas-Brown, Perturbation classes for semi-Fredholm operators on subprojective and superprojective spaces, Ann. Acad. Sci. Fenn. Math. 36 (2011), no. 2, 481–491. MR 2865508, DOI 10.5186/aasfm.2011.3625
H. Elton Lacey, The isometric theory of classical Banach spaces, Die Grundlehren der mathematischen Wissenschaften, Band 208, Springer-Verlag, New York-Heidelberg, 1974. MR 0493279, DOI 10.1007/978-3-642-65762-7
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
Heinrich P. Lotz, N. T. Peck, and Horacio Porta, Semi-embeddings of Banach spaces, Proc. Edinburgh Math. Soc. (2) 22 (1979), no. 3, 233–240. MR 560985, DOI 10.1017/S0013091500016394
T. Oikhberg and E. Spinu, Subprojective Banach spaces, J. Math. Anal. Appl. 424 (2015), no. 1, 613–635. MR 3286583, DOI 10.1016/j.jmaa.2014.11.008
A. Pełczyński and Z. Semadeni, Spaces of continuous functions. III. Spaces $C(\Omega )$ for $\Omega$ without perfect subsets, Studia Math. 18 (1959), 211–222. MR 107806, DOI 10.4064/sm-18-2-211-222
Raymond A. Ryan, Introduction to tensor products of Banach spaces, Springer Monographs in Mathematics, Springer-Verlag London, Ltd., London, 2002. MR 1888309, DOI 10.1007/978-1-4471-3903-4
Zbigniew Semadeni, Banach spaces of continuous functions. Vol. I, Monografie Matematyczne, Tom 55, PWN—Polish Scientific Publishers, Warsaw, 1971. MR 0296671
R. J. Whitley, Strictly singular operators and their conjugates, Trans. Amer. Math. Soc. 113 (1964), 252–261. MR 177302, DOI 10.1090/S0002-9947-1964-0177302-2