# A class of Banach sequence spaces analogous to the space of Popov

Czechoslovak Mathematical Journal (2009)

- Volume: 59, Issue: 3, page 573-582
- ISSN: 0011-4642

## Access Full Article

top## Abstract

top## How to cite

topAzimi, Parviz, and Ledari, A. A.. "A class of Banach sequence spaces analogous to the space of Popov." Czechoslovak Mathematical Journal 59.3 (2009): 573-582. <http://eudml.org/doc/37942>.

@article{Azimi2009,

abstract = {Hagler and the first named author introduced a class of hereditarily $l_1$ Banach spaces which do not possess the Schur property. Then the first author extended these spaces to a class of hereditarily $l_p$ Banach spaces for $1\le p<\infty $. Here we use these spaces to introduce a new class of hereditarily $l_p(c_0)$ Banach spaces analogous of the space of Popov. In particular, for $p=1$ the spaces are further examples of hereditarily $l_1$ Banach spaces failing the Schur property.},

author = {Azimi, Parviz, Ledari, A. A.},

journal = {Czechoslovak Mathematical Journal},

keywords = {Banach spaces; Schur property; hereditarily $l_p$; Banach space; Schur property; hereditarily },

language = {eng},

number = {3},

pages = {573-582},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {A class of Banach sequence spaces analogous to the space of Popov},

url = {http://eudml.org/doc/37942},

volume = {59},

year = {2009},

}

TY - JOUR

AU - Azimi, Parviz

AU - Ledari, A. A.

TI - A class of Banach sequence spaces analogous to the space of Popov

JO - Czechoslovak Mathematical Journal

PY - 2009

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 59

IS - 3

SP - 573

EP - 582

AB - Hagler and the first named author introduced a class of hereditarily $l_1$ Banach spaces which do not possess the Schur property. Then the first author extended these spaces to a class of hereditarily $l_p$ Banach spaces for $1\le p<\infty $. Here we use these spaces to introduce a new class of hereditarily $l_p(c_0)$ Banach spaces analogous of the space of Popov. In particular, for $p=1$ the spaces are further examples of hereditarily $l_1$ Banach spaces failing the Schur property.

LA - eng

KW - Banach spaces; Schur property; hereditarily $l_p$; Banach space; Schur property; hereditarily

UR - http://eudml.org/doc/37942

ER -

## References

top- Azimi, P., A new class of Banach sequence spaces, Bull. of Iranian Math. Society 28 (2002), 57-68. (2002) Zbl1035.46006MR1992259
- Azimi, P., Hagler, J., 10.2140/pjm.1986.122.287, Pacific J. Math. 122 (1986), 287-297. (1986) MR0831114DOI10.2140/pjm.1986.122.287
- Bourgain, J., ${\ell}_{1}$-subspace of Banach spaces, Lecture notes. Free University of Brussels.
- Lindenstrauss, J., Tzafriri, L., Classical Banach Spaces, Vol. I sequence Spaces, Springer Verlag, Berlin. Zbl0852.46015MR0415253
- Popov, M. M., 10.1090/S0002-9939-05-07758-0, Proc. Amer. Math. Soc. 133 (2005), 2023-2028. (2005) Zbl1080.46007MR2137868DOI10.1090/S0002-9939-05-07758-0
- Popov, M. M., More examples of hereditarily ${\ell}_{p}$ Banach spaces, Ukrainian Math. Bull. 2 (2005), 95-111. (2005) Zbl1166.46304MR2172327

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.