On the geometric properties of Cesàro spaces
Sbornik. Mathematics, Tome 203 (2012) no. 4, pp. 514-533 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is proved that the Cesàro space $\operatorname{Ces}_{p}[0,1]$, $1\le p<\infty$, contains a complemented subspace isomorphic to $l^q$ if and only if either $q=1$ or $q=p$. A class of subspaces of this space that contain complemented copies of the space $l^p$ is distinguished. Bibliography: 16 titles.
Keywords: Banach lattices, complemented subspaces, copies of $l^q$-spaces, sublinear operators.
Mots-clés : Cesàro spaces
@article{SM_2012_203_4_a2,
     author = {S. V. Astashkin},
     title = {On the geometric properties of {Ces\`aro} spaces},
     journal = {Sbornik. Mathematics},
     pages = {514--533},
     year = {2012},
     volume = {203},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2012_203_4_a2/}
}
TY  - JOUR
AU  - S. V. Astashkin
TI  - On the geometric properties of Cesàro spaces
JO  - Sbornik. Mathematics
PY  - 2012
SP  - 514
EP  - 533
VL  - 203
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_2012_203_4_a2/
LA  - en
ID  - SM_2012_203_4_a2
ER  - 
%0 Journal Article
%A S. V. Astashkin
%T On the geometric properties of Cesàro spaces
%J Sbornik. Mathematics
%D 2012
%P 514-533
%V 203
%N 4
%U http://geodesic.mathdoc.fr/item/SM_2012_203_4_a2/
%G en
%F SM_2012_203_4_a2
S. V. Astashkin. On the geometric properties of Cesàro spaces. Sbornik. Mathematics, Tome 203 (2012) no. 4, pp. 514-533. http://geodesic.mathdoc.fr/item/SM_2012_203_4_a2/

[1] M. Mastyło, “Banach spaces via sublinear operators”, Math. Japon., 36:1 (1991), 85–92 | MR | Zbl

[2] A. A. Jagers, “A note on Cesàro sequence spaces”, Nieuw Arch. Wisk. (3), 22 (1974), 113–124 | MR | Zbl

[3] B. I. Korenblyum, S. G. Krein, V. Ya. Levin, “O nekotorykh nelineinykh voprosakh teorii singulyarnykh integralov”, Dokl. AN SSSR, 62 (1948), 17–20 | MR | Zbl

[4] W. Wnuk, Banach lattices with order continuous norms, Polish Scientific Publ., Warszawa, 1999 | Zbl

[5] F. Albiac, N. J. Kalton, Topics in Banach space theory, Grad. Texts in Math., 233, Springer-Verlag, New York, 2006 | MR | Zbl

[6] M. I. Kadec, A. Pełczyński, “Bases, lacunary sequences and complemented subspaces in the spaces $L_p$”, Studia Math., 21 (1962), 161–176 | MR | Zbl

[7] S. V. Astashkin, L. Maligranda, “Structure of Cesàro function spaces”, Indag. Math. (N.S.), 20:3 (2009), 329–379 | DOI | MR | Zbl

[8] S. V. Astashkin, L. Maligranda, “Cesàro function spaces fail the fixed point property”, Proc. Amer. Math. Soc., 136:12 (2008), 4289–4294 | DOI | MR | Zbl

[9] L. V. Kantorovich, G. P. Akilov, Functional analysis, Pergamon Press, Oxford, 1982 | MR | MR | Zbl | Zbl

[10] S. G. Krejn, Yu. I. Petunin, E. M. Semenov, Interpolation of linear operators, Transl. Math. Monogr., 54, Amer. Math. Soc., Providence, RI, 1982 | MR | MR | Zbl | Zbl

[11] J. Lindenstrauss, L. Tzafriri, Classical Banach spaces, v. II, Ergeb. Math. Grenzgeb., 97, Function spaces, Springer-Verlag, Berlin–Heidelberg–New York, 1979 | MR | Zbl

[12] W. A. J. Luxemburg, A. C. Zaanen, “Some examples of normed Köthe spaces”, Math. Ann., 162:3 (1965/1966), 337–350 | DOI | MR | Zbl

[13] S. V. Astashkin, L. Maligranda, “Rademacher functions in Cesàro type spaces”, Studia Math., 198:3 (2010), 235–247 | DOI | MR | Zbl

[14] J. Bergh, J. Löfström, Interpolation spaces. An introduction, Springer-Verlag, Berlin–Heidelberg–New York, 1976 | MR | MR | Zbl

[15] M. Levy, “L'espace d'interpolation réel $(A_0,A_1)_{\theta,p}$ contient $\ell^p$”, C. R. Acad. Sci. Paris Sér. A-B, 289:14 (1979), 675–677 | MR | Zbl

[16] S. V. Astashkin, “Geometrical properties of Banach spaces generated by sublinear operators”, Positivity, 2012, Online First | DOI