Document Type : Research Paper

Authors

Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.

Abstract

We extend the class of Banach sequence spaces constructed by Ledari, as presented in ''A class of hereditarily $\ell_1$ Banach spaces without Schur property'' and obtain a new class of hereditarily $\ell_p(c_0)$ Banach spaces for $1\leq p<\infty$. Some other properties of this spaces are studied.

Keywords

Main Subjects

###### ##### References
[1] P. Azimi and J. Hagler, Examples of hereditarily $ell_1$ Banach spaces failing the Schur property, Pacific J. of Math., 122 (1986), pp. 287-297.

[2] P. Azimi and A.A. Ledari, A class of Banach sequence spaces analogous to the space of Popov, Czech. Math. J., 59 (2009), pp. 573-582.

[3] J. Bourgain, $ell_1$-subspace of Banach spaces, Lecture notes, Free University of Brussels.

[4] A.A. Ledari, A class of hereditarily $ell_p$ Banach spaces without Schur property, Iranian Journal of Science and Technology, 42 (2018), pp. 1-4.

[5] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces. I. Sequence spaces, Springer Verlag, Berlin, 1977.

[6] S.M. Moshtaghioun, Nowhere Schur property in some Operator spaces, Int. Journal of Math. Analysis, 4 (2010), pp. 1929-1936.

[7] M.M. Popov, A hereditarily $ell_1$ subspace of $L_1$ without the Schur property, Proc. Amer. Math. Soc., 133 (2005), pp. 2023-2028.

[8] M.M. Popov, More examples of hereditarily $ell_{p}$ Banach spaces, Ukrainian Math. Bull., 2 (2005), pp. 95-111.